Questions: Find m angle ABC.

Transcript text: Find $m \angle A B C$.

Solution

Solution Steps

Step 1: Find the measure of angle CAB

The angles $13x+6$ and $ \angle CAB $ are supplementary, so their measures add up to 180 degrees. $ m\angle CAB + 13x + 6 = 180 $ $ m\angle CAB = 180 - (13x+6) $ $ m\angle CAB = 174 - 13x $

Step 2: Find the measure of angle ACB

The angles $70^{\circ}$ and $\angle ACB$ are supplementary, so their measures add up to 180 degrees. $ m\angle ACB + 70 = 180 $ $ m\angle ACB = 180 - 70 $ $ m\angle ACB = 110 $

Step 3: Find the value of x

The sum of the angles in triangle ABC is 180 degrees. $m\angle ABC + m\angle ACB + m\angle CAB = 180$ $ 8 + 3x + 110 + 174 - 13x = 180 $ $ 292 - 10x = 180 $ $ -10x = 180 - 292 $ $ -10x = -112 $ $ x = \frac{-112}{-10} $ $ x = 11.2 $

Step 4: Calculate the measure of angle ABC.

$ m\angle ABC = 8 + 3x $ $ m\angle ABC = 8 + 3(11.2) $ $ m\angle ABC = 8 + 33.6 $ $ m\angle ABC = 41.6 $