Question

In triangle $XYZ$, $XZ=YZ$. If the measure of angle $Z$ has $a^o$, how many degrees are there in the measure of angle $X$?

• A. $x^o=\frac{{180}^o-2a}{2}$
• B. $x^o=\frac{{180}^o-a^o}{2}$
• C. $x^o=\frac{{180}^o-3a}{3}$
• D. none of these

Answer 1

The correct option is B $x^o=\frac{{180}^o-a^o}{2}$

Given, $XZ=YZ$ which implies angles $ZXY$ and $ZYX$ are equal and let it be $\theta$.
We have $ZXY+ZYX+XZY=180$ , which implies $\theta +\theta +a=180$
Which implies $\theta =\frac{(180-a)}{2}$