Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

varsity tutors app store varsity tutors android store

Example Questions

Example Question #531 : Triangles

Find the measurement of .

10

Possible Answers:

Correct answer:

Explanation:

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures  degrees.

Thus, for the triangle in question,

Example Question #21 : How To Find An Angle In A Right Triangle

Find the measurement of .

11

Possible Answers:

Correct answer:

Explanation:

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures  degrees.

Thus, for the triangle in question,

Example Question #23 : How To Find An Angle In A Right Triangle

Find the measurement of .

12

Possible Answers:

Correct answer:

Explanation:

Recall that the angles inside of a triangle must add up to . The small square in the corner of the triangle indicates that it is a right angle that measures  degrees.

Thus, for the triangle in question,

Example Question #21 : How To Find An Angle In A Right Triangle

A right triangle has equal legs of , and a hypotenuse of . Find the area. 

Possible Answers:

Correct answer:

Explanation:

The equation to find the area of a triangle is: 

In this problem, both the base and the height are 6in. By plugging in the numbers, we get 

Example Question #21 : How To Find An Angle In A Right Triangle

A right triangle has another angle that is 47 degrees. What is the third angle?

Possible Answers:

Correct answer:

Explanation:

The inside of a triangle has three angles that total 180 degrees. If one is 47 and the other is the right angle (90).

Then

.

To find the missing angle subtract the sum above from 180.

 is the degree measurement for the third angle.

Example Question #26 : How To Find An Angle In A Right Triangle

If one angle of a right triangle measures , what is the measure of its adjacent angle?

Possible Answers:

Correct answer:

Explanation:

First we need to know that no matter what type of triangle it is, when we add up the measures of all three angles, the total is .  The definition of a right triangle states that one of the three angles measures . In this problem we know that one of the angles measures  so we add that to  to get a sum of . To find our missing angle measure we must subtract the sum of the other two angles from the total, giving us an equation that looks like this. 

So our final answer is 

Example Question #27 : How To Find An Angle In A Right Triangle

Untitled

Refer to the above figure.

True or false: .

Possible Answers:

False

True

Correct answer:

False

Explanation:

If , then  is a 30-60-90 triangle. By the 30-60-90 Triangle Theorem, it would follow that hypotenuse  would be twice as long as shorter leg  - that is, 

,

However, since  and , then, substituting, 

.

It follows that .

Example Question #22 : How To Find An Angle In A Right Triangle

If one angle of a right triangle is  what is the measure of the third angle?

Possible Answers:

Correct answer:

Explanation:

First we need to know that when we add up all 3 angles of a triangle, the sum will always equal  (this is the case for all types of triangles). Since we know this is a right triangle, first we subtract  (by definition all right triangles equal ). 

 

We know another angle equals  so we subtract it from  and we get .

Our final answer is .

To check our answer we can add up the three angles to make sure we come up with a sum of 

 

Example Question #22 : How To Find An Angle In A Right Triangle

Untitled

True or false: 

Possible Answers:

False

True

Correct answer:

True

Explanation:

By the 30-60-90 Triangle Theorem, the ratio of the length of the longer leg of a 30-60-90 triangle to that of the shorter leg is . In the given triangle, we see that this ratio is

,

the correct ratio. This is indeed a 30-60-90 triangle, and,  being opposite the longer leg, has measure .

Example Question #543 : Triangles

A right triangle has side lengths of 5, 10, and 11.18 inches. One angle is 63.4 degrees. What is the measure of the other angle?

Possible Answers:

None of these.

Correct answer:

Explanation:

Since this is a right triangle, simply add this right angle to the given angle and subtract from 180 degrees.

The side lengths are not relevant in this problem.

Learning Tools by Varsity Tutors