Question

8. In the accompanying diagram of isosceles triangle ABC, AB = BC, m

Answer 1

In the given Isosceles triangle,

AB = BC

Since, from the property of issoceles triangle

Angle opposite to equal sides of a triangle are always equal,

So, in the given figure

Angle Opposite to side AB is angle C

Angle Opposite to side BC is angle A

so, Angle A = Angle C

$\begin{gathered} \angle A=\angle C \\ \text{ Since, it is given that }\angle A=x^{\circ} \\ So,\text{ }\angle C=\angle A=x^{\circ} \end{gathered}$

The sum of all angles in a triangle is equal to 180 degrees

$\begin{gathered} In\text{ triangle ABC} \\ \angle A+\angle B+\angle C=180^{\circ} \\ x^{\circ}+(x+30)^{\circ}+x^{\circ}=180^{\circ} \\ x^{\circ}+x^{\circ}+30^{\circ}+x^{\circ}=180^{\circ} \\ 3x^{\circ}+30^{\circ}=180^{\circ} \\ 3x^{\circ}=180^{\circ}-30^{\circ} \\ 3x^{\circ}=150^{\circ} \\ x^{\circ}=\frac{150^{\circ}}{3} \\ x^{\circ}=50^{\circ} \end{gathered}$

Answer : b) x = 50