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)=(150^(\circ))/(3) \\ x^(\circ)=50^(\circ) \end{gathered}`

Answer : b) x = 50