Question

A triangle includes one angle that 72º. Which pair could be the measures of the other two angles of the triangle?

A. 9º, 9º
B. 26º, 46º
C. 53º, 55º
D. 72º, 108º

Answer 1

C. 53º, 55º

Explanation:

The sum of interior angles of a triangle is 180°.

If one of the angles is 72°, the sum of the other two should be = 180° - 72°

= 108°

Testing the choices given;

A. 9º, 9º ⇒ 9+9 =18 Not correct

B. 26º, 46º ⇒ 26+46 = 72 Not correct

C. 53º, 55º ⇒ 53 + 55 = 108° Correct

The answer is C. 53º, 55º

Answer 2

Answer: C. 53º, 55º

Explanation:

1. By definition, the sum of the interior angles of a triangle is 180 degrees.

2. Keeping this on mind, you have:

`180\°-72\°=108\°`

As you can see, the sum of the other two angles must be 108 degrees, then, let's add the angles given in each option:

A. 9°+9°=18

B. 26°+46°=72°

C. 53°+55°=108°

D. 72°+108°=180°

3. Therefore, the answer is the option C.