Question

The vertical angle of an isosceles triangle is three times the sum of its base angles. Find each angle.

Answer 1

Step: Find all angles of triangle

Let each base angle of triangle = x

⇒ Vertical angle of a triangle = 3(x+x)

= 3×2x = 6x

∴ x + x + 6x = ${180}^{\circ }$

[ ∵ Angle sum property of a triangle]

8x = ${180}^{\circ }$

∴ x = $\frac{{180}^{\circ }}{8}$ = ${22.5}^{\circ }$

Hence, each base angle is ${22.5}^{\circ }$ and vertical angle is ${135}^{\circ }$.