1 Answer

AdorableVB · Answer 1 · 2020-08-29T08:31:41+0000

Answer:

x = 70°

Explanation:

Look at the picture.

We know: the sum of the angles measure in the triangle is 180°. Therefore we have the equation:

$35^o+35^o+\alpha=180^o$

Solve it:

$70^o+\alpha=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\\alpha=110^o$

Angle α and β = x are the supplementary angles. Supplementary angles add up to 180°. Therefore:

$\alpha+\beta=180^o$

$110^o+\beta=180^o\qquad\text{subtract}\ 110^o\ \text{from both sides}\\\\\beta=70^o$

$\beta+\gamma+\gamma=180^o$

$70^o+2\gamma=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\2\gamma=110^o\qquad\text{divide both sides by 2}\\\\\gamma=55^o$