Chapter 7.2, Problem 20PSD

Solution

To Calculate: Angle “ a ” in terms of “ b ” and “ c ”.

The required term is $\angle a={180}^{\circ }-2\angle b$

Given information: $\Delta RST$ is equiangular.

Formula used: Here, we are using the concept of angle sum property.

Calculation: Here, RS=ST=TR (equilateral triangle)

And, GH=KH (given)

Hence, $\angle HKG=\angle KGH$ (angle opposite to equal sides are equal)

Or, $\angle b=\angle c$

And, $\angle a+\angle b+\angle c={180}^{\circ }$ (angle sum property)

➔ $\angle a+2\angle b={180}^{\circ }$

So, $\angle a={180}^{\circ }-2\angle b$