Answer:
x = 70°
y = 55°
z = 55°
Step-by-step explanation:
Look at the picture.
We know: the sum of the angles measure in the triangle is 180°. Therefore we have the equation:
[tex]35^o+35^o+\alpha=180^o[/tex]
Solve it:
[tex]70^o+\alpha=180^o\qquad\text{subtract}\ 70^o\ \text{from both sides}\\\\\alpha=110^o[/tex]
Angle α and β = x are the supplementary angles. Supplementary angles add up to 180°. Therefore:
[tex]\alpha+\beta=180^o[/tex]
[tex]110^o+\beta=180^o\qquad\text{subtract}\ 110^o\ \text{from both sides}\\\\\beta=70^o[/tex]
[tex]\beta+\gamma+\gamma=180^o[/tex]
[tex]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[/tex]
