Question

Find the value of X

A.66

B.58

C.32

D.68

Answer 1

1) Δ ABC

m∠B + m∠C + m∠BAC = 180⁰

2) m∠DAB + m∠BAC = 180⁰ because m∠DAB and m∠BAC are supplementary angles.

3) m∠B + m∠C + m∠BAC = m∠DAB + m∠BAC

m∠B + m∠C = m∠DAB

32⁰ + x = 98⁰

x=98 - 32 = 66 ⁰

Answer: A. 66⁰.

Answer 2

Answer: Option A, 66°

Explanation:

Here we should use two things:

1) the addition of the 3 interior angles of a triangle always is equal to 180°

2) If a line cuts anoter line, two consecutive angles always add to 180°

now, we can see that the angle DA = 98°

then the angle AC can be obtained as:

AC = 180° - 98° = 82°

Now, with two of the interior angles of the triangle, we can find the other:

a + b + c = 180°

82° + 32° + c = 180°

c = 180° - 32° - 82° = 66°

so the correct option is the option A