Question

In triangle ABC, m∠A=(6x+9)∘, m∠B=(x−8)∘, and the exterior angle at C is 141∘.

What is the measure of angle B?
12∘
20∘
141∘
129∘

Answer 1

12

Explanation:

Answer 2

12°

Explanation:

Let's start with the easy first.

We know that m∠C is 39° because together ∠C and the exterior angle equal 180°. And 180 - 141 = 39.

Now, we can use this to find the remaining two angles.

180° - 39° = 141°

So, this means that we can set up m∠A + m∠B = 141°.

6x + 9 + x - 8 = 141

7x + 1 = 141

7x = 140

x = 20

Finally, we can plug in for our x value and find m∠B.

m∠B = x - 8

m∠B = 20 - 8

m∠B = 12°