Question

In ∆abc, m∠cab = 2x and m∠​acb = x + 30. if line segment a b is extended through point b to point d, m∠​cbd = 5x − 50. what is the value of x? 1. 25 2. 30 3. 40 4. 46

Answer 1

The answer is option "3, 40".

m∠cab = 2x
m∠​acb = x + 30
m∠​cbd = 5x − 50
Now,
m∠cab + m∠​acb = m∠​cbd
2x+x+30 = 5x-50
2x+x-5x = -50-30
-2x = -80
x = 40