Question

In a triangle ABC, angle A is half of B and angle C is thrice of A. Find the value of angle A, B and C? [4 MARKS]

Answer 1

Concept: 1 Mark
Framing of the equation: 1 Mark
Steps: 1 Mark
Result: 1 Mark

Let the value of angle B be $y^{\circ }$

Then, value of angle $A=\frac{y^{\circ }}{2}$

And, value of angle $C=\frac{3y^{\circ }}{2}$

We know that sum of all angles in a triangle is ${180}^{\circ }$.

$\Rightarrow y^{\circ }+\frac{y^{\circ }}{2}+\frac{3y^{\circ }}{2}={180}^{\circ }$

$\Rightarrow 3y^{\circ }={180}^{\circ }$

$\Rightarrow y^{\circ }={60}^{\circ }=$ Value of angle B

So, Value of angle $A=\frac{y^{\circ }}{2}={30}^{\circ }$

Value of angle $C=\frac{3y^{\circ }}{2}={90}^{\circ }$.