Question

Pls help me!! this is for a study guide :)

Answer 1

Answer:

x° = 149°

Step-by-step explanation:

According to the Triangle Sum Theorem, the sum of the measures of the angles in every triangle is 180°. Since we are given two angles with measures of m < 86° and m < 63°, then the third angle must be:

m < 86° + m < 63° + m < (angle 3) = 180°

149° + m < ? = 180°

Subtract 149° from both sides to solve for m < (angle 3)

149° - 149° + m < (angle 3)   = 180° - 149°

m < ?   = 31°

Therefore, the measure of the third angle is 31°.

To find x°, we can reference the Triangle Exterior Angle Postulate, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

In other words, the measure of x° = m < 86° + m < 63°

x° = 149°

By the way, m< (angle 3) and x° are also supplementary angles whose sum equal 180°:

x° + m < (angle 3) = 180°

149° +  31° = 180°