Question

Please help!
How would I solve number 4 with the variables of x,y, and z?

Answer 1

Answer:

$\huge\boxed{x^o=67^o,\ y^o=113^o,\ z^o=52^o}$

Step-by-step explanation:

$\text{We know:}\\\text{The angles in each triangles add up to 180}^o.$

$\text{In the triangle ABC:}\\\\85+28+15+z=180\\128+z=180\qquad\text{subtract 128 from both sides}\\128-128+z=180-128\\\boxed{z=52}$

$\\\\\text{In the triangle ADC}:\\\\85+28+x=180\\113+x=180\qquad\text{subtract 113 from both sides}\\113-113+x=180-113\\\boxed{x=67}$

$\text{In the triangle DBC:}\\\\y+52+15=180\\y+67=180\qquad\text{subtract 67 from both sides}\\y+67-67=180-67\\\boxed{y=113}$