Question

3. In triangle ABC, m<BAC = 4x + 10, m<ABC = 5x + 18, and m<BCA = 3x - 16. (a) Find the value of x. (b) Find the measure of <3.

Answer 1

(a) Find the value of x.

Sum of interior in a triangle = 180

So m<BAC  + m<ABC + m<BCA = 180

4x + 10 + 5x + 18 + 3x - 16 = 180

12x + 12 = 180

12x = 168

  x = 14

(b) Find the measure of <3.

<3 + <BCA = 180

<BCA = 3x - 16 = 3(14) - 16 = 26°

So

<3 = 180 - <BCA

<3 = 180 - 26

<3 = 154°