In isosceles triangle $R S T$ , $\overline { R S } \cong \overline { S T }$ . If $m \angle T = 2 ( x + 3 )$ and $m \angle S = 3 x$ , find the value of x .
A) $x = 24$
B) $x = 32$
C) $x = 46$
D) $x = 58$

Question

Quizplus · Accepted Answer

In an isosceles triangle, the angles opposite the equal sides are equal. Therefore, $m \angle R = m \angle T$. Since the sum of angles in a triangle is $180^\circ$, we have $m \angle R + m \angle S + m \angle T = 180$. Substituting $m \angle T = 2(x + 3)$ and $m \angle S = 3x$, and knowing $m \angle R = m \angle T$, we get $2(x + 3) + 3x + 2(x + 3) = 180$. Solving this equation gives $x = 24$.

In Isosceles Triangle RSTR S TRST RS‾≅ST‾\overline { R S } \cong \overline { S T }RS≅ST

In Isosceles Triangle $R S T$ $\overline { R S } \cong \overline { S T }$