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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

In ΔABC, A = 75°, a = 13, and b = 6.

Find B (to the nearest tenth).

Possible Answers:

34.9°

26.5°

28.1°

30.4°

27.8°

Correct answer:

26.5°

Explanation:

This problem requires us to use either the Law of Sines or the Law of Cosines. To figure out which one we should use, let's write down all the information we have in this format:

A = 75° a = 13

B = ? b = 6

C = ? c = ?

Now we can easily see that we have a complete pair, A and a. This tells us that we can use the Law of Sines. (We use the Law of Cosines when we do not have a complete pair).

Law of Sines:
$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

To solve for b, we can use the first two terms which gives us:
$\frac{\sin 75°}{13}=\frac{\sin B°}{6}$
$\sin B =6*\frac{\sin 75}{13}$
B=26.5°

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Example Question #531 : Plane Geometry

Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{\circ}$ . The measure of angle CBD is $60^{\circ}$ . The length of segment $\overline{AD}$ is 4.

Find the measure of $\dpi{100} \small \angle ADB$ .

Possible Answers:

$15^{\circ}$

$60^{\circ}$

$90^{\circ}$

$45^{\circ}$

$30^{\circ}$

Correct answer:

$30^{\circ}$

Explanation:

The measure of $\dpi{100} \small \angle ADB$ is $30^{\circ}$ . Since $\dpi{100} \small A$ , $\dpi{100} \small B$ , and $\dpi{100} \small C$ are collinear, and the measure of $\dpi{100} \small \angle CBD$ is $60^{\circ}$ , we know that the measure of $\dpi{100} \small \angle ABD$ is $120^{\circ}$ .

Because the measures of the three angles in a triangle must add up to $180^{\circ}$ , and two of the angles in triangle $\dpi{100} \small ABD$ are $30^{\circ}$ and $120^{\circ}$ , the third angle, $\dpi{100} \small \angle ADB$ , is $30^{\circ}$ .

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Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

The largest angle in an obtuse scalene triangle is 120 degrees. The second largest angle in the triangle is $\frac{1}{3}$ the measurement of the largest angle. What is the measurement of the smallest angle in the obtuse scalene triangle?

Possible Answers:

$15^\circ$

$40^\circ$

$25^\circ$

$20^\circ$

$30^\circ$

Correct answer:

$20^\circ$

Explanation:

Since this is a scalene triangle, all of the interior angles will have different measures. However, it's fundemental to note that in any triangle the sum of the measurements of the three interior angles must equal 180 degrees.

The largest angle is equal to 120 degrees and second interior angle must equal:

$120\div3=40$

120+40=160

Therefore, the final angle must equal:

180-160=20

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Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

In an obtuse isosceles triangle the largest angle is 133 degrees. Find the measurement of one of the two equivalent interior angles.

Possible Answers:

$24^\circ$

$47^\circ$

$23\frac{1}{2}^\circ$

$47\frac{1}{2}^\circ$

$31^\circ$

Correct answer:

$23\frac{1}{2}^\circ$

Explanation:

An obtuse isosceles triangle has one obtuse interior angle and two equivalent acute interior angles. Since the sum total of the interior angles of every triangle must equal 180 degrees, the solution is:

180-133=47

$47\div2=23\frac{1}{2}$

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Example Question #3 : How To Find An Angle In An Acute / Obtuse Triangle

In an acute scalene triangle the measurement of the interior angles range from degrees to degrees. Find the measurement of the median interior angle.

Possible Answers:

$69^\circ$

$67^\circ$

$72^\circ$

$12^\circ$

$47^\circ$

Correct answer:

$67^\circ$

Explanation:

Acute scalene triangles must have three different acute interior angles--which always have a sum of 180 degrees.

Thus, the solution is:

79+34=113

180-113=67

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Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

The largest angle in an obtuse scalene triangle is 115 degrees. The smallest interior angle is $\frac{1}{5}$ the measurement of the largest interior angle. Find the measurement of the third interior angle.

Possible Answers:

$42^\circ$

$23^\circ$

$44^\circ$

$38^\circ$

$46^\circ$

Correct answer:

$42^\circ$

Explanation:

An obtuse scalene triangle must have one obtuse interior angle and two acute angles.

Therefore the solution is:

$115\div5=23$

115+23=138

All triangles have three interior angles with a sum total of 180 degrees.

Thus,

180-138=42

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Example Question #7 : How To Find An Angle In An Acute / Obtuse Triangle

The largest angle in an obtuse isosceles triangle is degrees. Find the measurement for one of the equivalent acute interior angles.

Possible Answers:

$86^\circ$

$49^\circ$

$43^\circ$

$84^\circ$

$37^\circ$

Correct answer:

$43^\circ$

Explanation:

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Example Question #8 : How To Find An Angle In An Acute / Obtuse Triangle

In an acute isosceles triangle the largest interior angle is degrees. Find the measure for one of the two equivalent acute interior angles.

Possible Answers:

$39^\circ$

$46^\circ$

$49^\circ$

$44^\circ$

$48^\circ$

Correct answer:

$46^\circ$

Explanation:

The sum of the three interior angles in any triangle must equal 180 degrees. Therefore, the solution is:

180-88=92

$92\div 2= 46$

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Example Question #9 : How To Find An Angle In An Acute / Obtuse Triangle

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Find the value of .

Possible Answers:

$28^\circ$

$34^\circ$

$38^\circ$

$37^\circ$

$27^\circ$

Correct answer:

$38^\circ$

Explanation:

To find the value of , consider the fundamental notion that the sum of the three interior angles of any triangle must equal 180 degrees.

Thus, the solution is:

90+52=142

180-142=38

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Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

An obtuse isosceles triangle has an interior angle with a measure of 140 degrees.

Select the answer choice that displays the correct measurements for the two other interior angles of the triangle.

Possible Answers:

$10^\circ$ , $15^\circ$

$15^\circ$ , $25^\circ$

$30^\circ$ , $10^\circ$

$20^\circ$ , $20^\circ$

$20^\circ$ , $40^\circ$

Correct answer:

$20^\circ$ , $20^\circ$

Explanation:

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Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #531 : Plane Geometry

Example Question #1 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #3 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #7 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #8 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #9 : How To Find An Angle In An Acute / Obtuse Triangle

Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle

All Intermediate Geometry Resources

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