Question

In this figure, m∠3 = (2x + 15)° and m∠6 = (3x + 10)°. What value of x makes a∥b? Enter your answer in the box.

In △ABC, m∠A = (4x + 5)° and m∠B = (5x−1)° What is m∠C?

A.6°
B.29°

C.180°

D.122°

Answer 1

For First Question:
As, we find the value of x for parallel condition of line a and b
so, m∠3 = m∠1 and m∠2 = 180°-m∠1 = 180°-(2x+15)° [ As straight line contain total 180°]
Now,
m∠2 = m∠6 [ Because they are corresponding angles]
180-(2x+15)=(3x+10)
180=3x+10+2x+15
x= 31 satisfies the condition of a||b

For second Question:
As, it is issoceles triangle So side AC = side BC So, m∠A=m∠B
4x+5=5x-1
x=6
So,
m∠A=29° and triangle contain total 180°
m∠C=180-29-29
=122°
Option D is correct