Question

Two isosceles triangle are shown above. If $180-z=2y$ and $y={75}^o$, what is the value of $x$?

• A. ${105}^o$
• B. ${104}^o$
• C. ${103}^o$
• D. ${102}^o$

Answer 1

The correct option is A ${105}^o$

Given, $180-z=2y$ and $y={75}^o$

$\Rightarrow 180-z=150$

$\Rightarrow z=30$

Thus, each of the base angles of the isosceles triangle on the right has measure $\frac{180-30}{2}=75$ degrees.

Therefore, the measure of the angle marked $x$ degrees is $180-75={105}^o$ degrees and hence the value of $x$ is ${105}^o$.