Question

Question 137

In the given figure, if ST = SU, then find the values of x and y.

Answer 1

Given, ST = SU
$\therefore \angle SUT=\angle STU=y$ [$\because$ angles opposite to equal sides are equal]

Also, $\angle 1={78}^{\circ }$ [vertically opposite angles]
In $\Delta SUT,{78}^{\circ }+y+y={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow {78}^{\circ }+2y={180}^{\circ }\Rightarrow 2y={180}^{\circ }-{78}^{\circ }={102}^{\circ }\Rightarrow y=\frac{{102}^{\circ }}{2}={51}^{\circ }$
Also, $x+y={180}^{\circ }$ [linear pair]
$\Rightarrow x+{51}^{\circ }={180}^{\circ }\Rightarrow x={180}^{\circ }-{51}^{\circ }\Rightarrow x={129}^{\circ }$