Question

a triangle has two equal angles, each of which is equal to twice the remaining third angle. find the angles of the triangle.​

Answer 1

Answer:

Let the measure of third angle be x

According to the question, each of the remaining two angles are twice of x.

Third angle = x

Each equal angle = 2x

Sum of all angles of a triangle = 180°

x + 2x + 2x = 180°

5x = 180°

x = \dfrac{180 \degree}{5}x=

5

180°

x = 36°

Therefore, third angle = x = 36° and each equal angle = 2x = 2( 36° ) = 72°

Answer 2

Question :-

A triangle has two equal angles, each of which is equal to twice the remaining third angle. Find the angles of the triangle.

Solution :-

$\huge{\sf{\red{Given:-}}}$

• Triangle has two equal angles.
• Each of the equal angle is equal to twice the remaining third angle

$\huge{\sf{\red{Let:-}}}$

• The third angle of the traingle be x
• Each equal angles = 2x

$\huge{\sf{\red{We~know~that:-}}}$

• The sum of the angles of triangle is equal to 180°

______________________________________

• Using the Sum angle property of triangle;

$\bf{2x+2x+x=180°}$

$\bf{5x=180°}$

$\bf{x=\cancel\dfrac{180°}{5}}$

$\bf{x=36°}$

• We get x=36°

$\sf{\red{Now,The~angles~of~the~triangle~are:-}}$

$\sf{Equal~angle= 2x = 2(36°)}$

$\implies\sf{Equal~angles = 72°}$

$\sf{Third~angles = x = 36°}$