Find the value of in the triangle shown below.
0
=
80°
7
7
2
9

Possible Answers:

C=53

C=65

None of these

C=70

C=72

Correct

C=65

Explanation:

First, know that all the angles in a triangle add up to 180 degrees.

Each triangle has 3 angles. Thus, we have the sum of three angles as shown:

180=A+B+C

where we have angles A, B, and C. In our right triangle, one angle is 25 degree and we'll call that angle A. The other known angle is 90 degrees and we'll call this angle B. Thus, we have

180=25+90+C

Simplify and solve for C.

180=115+C

C=65

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Find An Angle In A Right Triangle : Example Question #2

Which of the following can be two angle measures of a right triangle?

Possible Answers:

38∘,42∘

60∘,60∘

100∘,10∘

35∘,55∘

60∘,40∘

Correct

35∘,55∘

Explanation:

A right triangle cannot have an obtuse angle; this eliminates the choice of 100 and 10.

The acute angles of a right triangle must total 90 degrees. Three choices can be eliminated by this criterion:

60+40=100

38+42=80

60+60=120

The remaining choice is correct: 35+55=90

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Find An Angle In A Right Triangle : Example Question #3

A right triangle has an angle that is 15 more than twice the other. What is the smaller angle?

Possible Answers:

20

15

30

25

10

Correct

25

Explanation:

The sum of the angles in a triangle is 180. A right triangle has one angle of 90. Thus, the sum of the other two angles will be 90.

Let x = first angle and 2x+15 = second angle

So the equation to solve becomes x+2x+15=90 or 3x=75

Thus, the first angle is 25 and the second angle is 65.

So the smaller angle is 25

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Find An Angle In A Right Triangle : Example Question #4

Angle A in the triangle shown below (not to scale) is 35 degrees. What is angle B?

Right_triangle_sides_and_points

Possible Answers:

90 degrees

35 degrees

55 degrees

125 degrees

Correct

55 degrees

Explanation:

The interior angles of a triangle always add up to 180 degrees. We are given angle A and since this is indicated to be a right triangle we know angle C is equal to 90 degrees. Thus we know 2 of the 3 and can determine the third angle.

180−35−90=55

Angle B is equal to 55 degrees.

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Find An Angle In A Right Triangle : Example Question #5

Which of the following cannot be true of a right triangle?

Possible Answers:

None of the other statements can be true of a right triangle.

One leg can be longer than the hypotenuse.

A right triangle can have an obtuse angle.

A right triangle can be equilateral.

The measures of the angles of a right triangle can total 160∘.

Correct

None of the other statements can be true of a right triangle.

Explanation:

All of these statements are false.

A right triangle can be equilateral.

False: An equilateral triangle must have three angles that measure 60∘ each.

One leg can be longer than the hypotenuse.

False: Each leg is shorter than the hypotenuse.

A right triangle can have an obtuse angle.

False: Both angles of a right triangle that are not right must be acute.

The measures of the angles of a right triangle can total 160∘.

False: The measures of any triangle total 180∘