Question

Find the measure of angle C of a triangle ABC, if: m∠A = α, m∠B = 2α Find m∠C

Answer 1

Answer:

180°- 3α

Step-by-step explanation:

By angle sum postulate of a triangle.

$m \angle \: A+ m \angle \: B + m \angle \: C = 180 \degree \\ \alpha + 2 \alpha + m \angle \: C = 180 \degree \\ 3 \alpha + m \angle \: C = 180 \degree \\ \huge \red{ \boxed{\angle \: C = 180 \degree - 3 \alpha}}$

Answer 2

In a triangle $ABC$ the measure of angle $C$ is equals to $(180 - 3\alpha )\°$.

What is triangle?

" Triangle is defined as the two dimensional geometrical shape with three sides , three vertices and three angles enclosed in it.Sum of all the interior angles in a triangle is equals to $180\°$. "

According to the question,

In a triangle $ABC$,

Given measure of angles,

$m\angle A = \alpha \\\\m\angle B = 2\alpha$

Sum of all the interior angles in a triangle is equals to $180\°$.

Therefore,

$m\angle A + m\angle B + m\angle C = 180\°$                               ________$(1)$

Substitute the value of  $m\angle A , m\angle B$  in $(1)$  we get,

$\alpha + 2 \alpha + m \angle C = 180\°\\\\\implies 3\alpha + m \angle C = 180\°\\\\\implies m \angle C = 180\°- 3\alpha$

Hence , in a triangle $ABC$ the measure of angle $C$ is equals to  $(180 - 3\alpha )\°$.

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