Home

Tutoring

Subjects

Live Classes

Study Coach

Essay Review

On-Demand Courses

Colleges

Games

Opening subject page...

Loading your content

Home

Tutoring

Subjects

Live Classes

Study Coach

Essay Review

On-Demand Courses

Colleges

Games

ACT Math

ACT Math Help: Lines And Angles

Review real example questions for Lines And Angles in ACT Math.

Question 1

In the diagram, lines $l$ and $m$ are parallel and are intersected by a transversal line $t$ . If the measure of angle 1 is $70°$ , what is the measure of angle 7?

$20°$
$70°$
$110°$
$160°$

Explanation: This is a parallel lines and transversals question testing supplementary angle relationships. Choice C (110°) is correct — using standard transversal labeling (angles 1–4 at the upper intersection, 5–8 at the lower), angles 1, 3, 5, and 8 are all congruent, and angles 2, 4, 6, and 8 are all supplementary to 1, 3, 5, and 8. So if angle 1 is 70, that mens that angle 8 is 70, and that means that angle 7 is 110.

Question 2

Two lines intersect. One of the angles formed is $120^\circ$ . Angle $x$ is adjacent to the $120^\circ$ angle, sharing a side with it, and the other sides form a straight line (a linear pair). What is the measure of angle $x$ ?

$240^\circ$
$120^\circ$
$30^\circ$
$60^\circ$

Explanation: The angles form a linear pair, being adjacent and forming a straight line. Linear pairs are supplementary, so their measures add to

180^\circ

. Subtract the given

120^\circ

from

180^\circ

: x =

180^\circ

120^\circ

60^\circ

. This applies the straight-angle property. Choice B of

120^\circ

might result from assuming equality instead of supplement.

Question 3

In the diagram, angle $A$ is a right angle. What is the measure of angle $A$ ?

45°
90°
180°
60°

Explanation: A right angle is defined as an angle that measures exactly 90°. This is a fundamental definition in geometry. By definition, any right angle has a measure of 90°. Choices A, C, and D represent acute, straight, and obtuse angles respectively.

Question 4

Lines $m$ and $n$ are parallel and cut by a transversal. An interior angle on the left side of the transversal at the top intersection is $70^\circ$ . The alternate interior angle at the bottom intersection is labeled $x$ .

   m  ⇒ ⇒ ⇒
     70°\
         \
          \
   n  ⇒ ⇒ ⇒
        / x

If lines $m$ and $n$ are parallel, what is the measure of angle $x$ ?

$110^\circ$
$70^\circ$
$20^\circ$
$90^\circ$

Explanation: The 70° angle and angle x are alternate interior angles created by a transversal intersecting parallel lines m and n. Alternate interior angles are equal in measure when the lines are parallel, as they lie on opposite sides of the transversal between the parallels. Therefore, angle x measures 70°. This property helps prove lines are parallel or find unknown angles in such configurations. Choice A of 110° might stem from incorrectly treating them as supplementary instead of alternate interior.

Question 5

In a pair of parallel lines cut by a transversal, angle $3$ is $85^\text{o}$ . What is the measure of angle $6$ , the alternate interior angle?

95°
85°
75°
90°

Explanation: Angles 3 and 6 are alternate interior angles formed by parallel lines cut by a transversal. When parallel lines are cut by a transversal, alternate interior angles are equal. Since angle 3 is 85°, angle 6 must also be 85°. Choice A incorrectly uses 95°, which has no geometric relationship to the given angle.

Question 6

In the diagram, a straight line forms a linear pair of adjacent angles. One angle measures $48^\circ$ , and the adjacent angle is labeled $x$ . What is the measure of angle $x$ ?

$132^\circ$
$42^\circ$
$48^\circ$
$90^\circ$

Explanation: The angles form a linear pair on a straight line. Angles in a linear pair are supplementary, meaning they add up to

180^\circ

. To find x, subtract the given

48^\circ

from

180^\circ

x \= 180^\circ - 48^\circ \= 132^\circ

. This calculation emphasizes the straight-line property. Choice C of

48^\circ

might confuse this with vertical angles, which are equal instead of supplementary.

Question 7

At point $O$ , two lines intersect. The angle labeled $48^\circ$ and the angle labeled $x$ are vertical angles.

   \ 48° /
    \   /
-----O-----
    / x  \

What is the measure of angle $x$ ?

$132^\circ$
$48^\circ$
$90^\circ$
$180^\circ$

Explanation: The angles 48° and x are vertical angles formed when two lines intersect at point O. Vertical angles are always equal because they are opposite each other when two lines cross. Therefore, x = 48°. Choice A (132°) incorrectly treats these as supplementary angles, which would be the relationship between adjacent angles on a straight line rather than vertical angles.

Question 8

Lines $p$ and $q$ are parallel, and line $r$ is a transversal. If angle $2$ is $110^\circ$ , what is the measure of the corresponding angle $4$ ?

70°
110°
80°
100°

Explanation: Angles

2

and

4

are corresponding angles formed by parallel lines p and q cut by transversal r. When parallel lines are cut by a transversal, corresponding angles are equal. Since angle

2

110^\circ

, angle

4

must also be

110^\circ

. Choice A incorrectly uses

70^\circ

, which would be the supplementary angle.

Question 9

Lines $m$ and $n$ are parallel (⇒). A transversal $t$ intersects them. The angle labeled $x$ is an exterior angle at line $n$ on the right side of the transversal. The angle labeled $95^\circ$ is the corresponding exterior angle at line $m$ on the right side of the transversal.

m  ⇒  ───────────────
            / 95°
           / t
          /
         /
        /  x
n  ⇒  ───────────────

If lines $m$ and $n$ are parallel, what is the measure of angle $x$ ?

$85^\circ$
$95^\circ$
$180^\circ$
$90^\circ$

Explanation: The angles x and 95° are corresponding angles formed by parallel lines m and n with transversal t. When two parallel lines are cut by a transversal, corresponding angles are always equal. Therefore, x = 95°. Choice A (85°) might result from incorrectly treating these as supplementary angles, which would be the case for same-side interior angles but not corresponding angles.

Question 10

In the diagram, lines $m$ and $n$ are parallel, cut by transversal $t$ . The angle labeled $40^\circ$ is above line $m$ and to the right of $t$ . Angle $x$ is above line $n$ and to the right of $t$ .

If lines $m$ and $n$ are parallel, what is the measure of angle $x$ ?

$140^\circ$
$40^\circ$
$90^\circ$
$180^\circ$

Explanation: The angles are corresponding angles formed by the transversal intersecting the parallel lines. When lines are parallel, corresponding angles are congruent and thus equal in measure. Since the given angle is 40°, angle x also measures 40°. This equality holds due to the parallel lines property. Choice A, 140°, might come from incorrectly treating the angles as supplementary.

Opening subject page...

Loading your content

ACT Math

ACT Math Help: Lines And Angles

Review real example questions for Lines And Angles in ACT Math.

Question 1

In the diagram, lines $l$ and $m$ are parallel and are intersected by a transversal line $t$ . If the measure of angle 1 is $70°$ , what is the measure of angle 7?

$20°$
$70°$
$110°$
$160°$

Question 2

$240^\circ$
$120^\circ$
$30^\circ$
$60^\circ$

Explanation: The angles form a linear pair, being adjacent and forming a straight line. Linear pairs are supplementary, so their measures add to

180^\circ

. Subtract the given

120^\circ

from

180^\circ

: x =

180^\circ

120^\circ

60^\circ

. This applies the straight-angle property. Choice B of

120^\circ

might result from assuming equality instead of supplement.

Question 3

In the diagram, angle $A$ is a right angle. What is the measure of angle $A$ ?

45°
90°
180°
60°

Question 4

   m  ⇒ ⇒ ⇒
     70°\
         \
          \
   n  ⇒ ⇒ ⇒
        / x

If lines $m$ and $n$ are parallel, what is the measure of angle $x$ ?

$110^\circ$
$70^\circ$
$20^\circ$
$90^\circ$

Question 5

In a pair of parallel lines cut by a transversal, angle $3$ is $85^\text{o}$ . What is the measure of angle $6$ , the alternate interior angle?

95°
85°
75°
90°

Question 6

In the diagram, a straight line forms a linear pair of adjacent angles. One angle measures $48^\circ$ , and the adjacent angle is labeled $x$ . What is the measure of angle $x$ ?

$132^\circ$
$42^\circ$
$48^\circ$
$90^\circ$

Explanation: The angles form a linear pair on a straight line. Angles in a linear pair are supplementary, meaning they add up to

180^\circ

. To find x, subtract the given

48^\circ

from

180^\circ

x \= 180^\circ - 48^\circ \= 132^\circ

. This calculation emphasizes the straight-line property. Choice C of

48^\circ

might confuse this with vertical angles, which are equal instead of supplementary.

Question 7

At point $O$ , two lines intersect. The angle labeled $48^\circ$ and the angle labeled $x$ are vertical angles.

   \ 48° /
    \   /
-----O-----
    / x  \

What is the measure of angle $x$ ?

$132^\circ$
$48^\circ$
$90^\circ$
$180^\circ$

Question 8

Lines $p$ and $q$ are parallel, and line $r$ is a transversal. If angle $2$ is $110^\circ$ , what is the measure of the corresponding angle $4$ ?

70°
110°
80°
100°

Explanation: Angles

2

and

4

are corresponding angles formed by parallel lines p and q cut by transversal r. When parallel lines are cut by a transversal, corresponding angles are equal. Since angle

2

110^\circ

, angle

4

must also be

110^\circ

. Choice A incorrectly uses

70^\circ

, which would be the supplementary angle.

Question 9

m  ⇒  ───────────────
            / 95°
           / t
          /
         /
        /  x
n  ⇒  ───────────────

If lines $m$ and $n$ are parallel, what is the measure of angle $x$ ?

$85^\circ$
$95^\circ$
$180^\circ$
$90^\circ$

Question 10

In the diagram, lines $m$ and $n$ are parallel, cut by transversal $t$ . The angle labeled $40^\circ$ is above line $m$ and to the right of $t$ . Angle $x$ is above line $n$ and to the right of $t$ .

If lines $m$ and $n$ are parallel, what is the measure of angle $x$ ?

$140^\circ$
$40^\circ$
$90^\circ$
$180^\circ$