Question

In Geometry Figure 32 below, $AC=BC$. Find the value of $x$ and $y$.

Answer 1

In $\Delta ABC$

$AC=BC$ ----- (i)

$\angle BAC=\angle ABC$

$\angle BAC={180}^{{}^{\circ }}-{125}^{{}^{\circ }}={55}^{{}^{\circ }}$

$\angle BAC={55}^{\circ }$ (adjacent angles)

$\angle ABC={55}^{\circ }$ (from (i))

In $\Delta ABC$

${55}^{\circ }+{55}^{\circ }+x^{\circ }={180}^{\circ }$

$x={70}^{\circ }$

$y={125}^{\circ }$ (adjacent angles property)