Question

$\Delta$BUG is an isosceles triangle with BU = GU. Find all the angles.

• A. ${50}^{\circ }$, ${50}^{\circ }$, ${80}^{\circ }$
• B. ${45}^{\circ }$, ${45}^{\circ }$, ${90}^{\circ }$
• C. ${60}^{\circ }$, ${30}^{\circ }$, ${90}^{\circ }$
• D. ${42}^{\circ }$, ${42}^{\circ }$, ${96}^{\circ }$

Answer 1

The correct option is D ${42}^{\circ }$, ${42}^{\circ }$, ${96}^{\circ }$

Given, BU = GU.
$\Rightarrow$ $\angle B$ = $\angle G$ [angles opposite to equal sides are equal]
$\Rightarrow$ $\angle G=(x+10{)}^{\circ }$
Sum of all angles in a triangle = ${180}^{\circ }$
$\Rightarrow$ $\angle B$ + $\angle U$ + $\angle G$ = ${180}^{\circ }$
$\Rightarrow x+10+3x+x+10={180}^{\circ }$
$\Rightarrow 5x+20={180}^{\circ }$
$\Rightarrow 5x={160}^{\circ }$
$\Rightarrow x={32}^{\circ }$
$\therefore x+10=32+10$
$\therefore x={42}^{\circ }$
$3x=3\times 32={96}^{\circ }$
$\therefore$ Angles of the given triangle are ${42}^{\circ }$, ${42}^{\circ }$ and ${96}^{\circ }$.