Question

In triangle ABC, angles A and B are equal and angle C is 20 degree more than the equal angles. Find the angle​

Answer 1

Let the measure of angle A be x .

Then angle B = x

Angle C = 2x + 20

The sum of all three of these angles = 180° (angle sum property)

This statement can be written in an equation as :-

$\hookrightarrow \: x \texttt{ \: + \: }x\texttt{ + }\texttt{2}x \texttt{ \: + \: }\texttt{20 \: = \: 180}$

Let us solve the equation to find the value of each of the angles of this triangle :-

$= x \texttt{ \: + \: } x \texttt{ \: + \: } 2x \texttt{ \: + \: }\texttt{20 = 180}$

$= \texttt{4}x \texttt{ + 20 = 180}$

$= \texttt{4}x\texttt{ = 180 - 20}$

$=\texttt{ 4}x \texttt{ \: = 160}$

$= x \texttt{ \: = \: } \frac{\texttt{160}}{\texttt{4}}$

$= \color{hotpink}x \texttt{ \: = \: 40}$

Which means :-

∠A = 40°

∠B = 40°

∠C :-

$\texttt{ = 40 + 40 + 20 }</p><p>$

$\texttt{</p><p>= 80 + 20}$

∠C = 100°

As the sum of all three angles is adding up to form 180°(40+40+100=180), we can conclude that we have found out the correct measures of the angles.

Therefore, the measure of :-

∠A = 40° , ∠B = 40° and ∠C = 100° .