Question

Each of the two equal angles of an isoceles triangle is twice the third angle . Find the angles of the triangle.​

Answer 1

Answer :-

Given :-

• Each equal angle are twice third angle

To Find :-

• All the angles of the traingle

Solution :-

Let the third angle be x

Each equal angle = 2x

Applying angle sum property in triangle -

⇒ x + 2x + 2x = 180°

⇒ 5x = 180

⇒ x = 180/5

⇒ x = 36

Third angle = 36°

Each equal angle = 36 × 2 = 72°

Angles of triangle = 36° , 72° , 72°

Verification :-

Sum of angles of triangle should be equal to 180°

Angles = 36° , 72° and 72°

⇒ 36 + 72 + 72 = 180

⇒ 144 + 36 = 180

⇒ 180 = 180

Hence verified.

Answer 2

Given :-

$~~~~~~~~$

• Each equal angle are twice third angle

$~~~~~~~$

To find :-

$~~~~~~~$

• All the angles of the triangle

$~~~~~~~$

Solution :-

$~~~~~~~$

• Let the third angle be x
• Each equal angle 2x

$~~~~~~~$

★ Applying angle sum property in triangle :

$~~~~~~~$

$\implies$ $\large{\sf{x + 2x + 2x = 180°}}$

$\implies$ $\large{\sf{5x = 180°}}$

$\implies$ x = $\large{\sf{\frac{180}{5} }}$

$\implies$ $\large{\sf{x = 36}}$

$~~~~~~~$

★ Third angle = 36°

★ Each equal angle = 36 × 2 = 72°

$~~~~~~~$

$\dag$ Angle of triangle = 36° , 72° , 72°

$~~~~~~~$

$~~~~~~~~~~~~~~~~~~$ ________________

$~~~~~~~~~~~~~~~~~~$ ★ Verification :

$~~~~~~~~~~~~~~~~~~$ ________________

$~~~~~~~~~$

$\dag$ Sum of angles of triangle should be equal to 180°

$~~~~~~~~~$

★ Angles 36° , 72° and 72°

$~~~~~~~~~$

$\implies$ 36 + 72 + 72 = 180

$\implies$ 144 + 36 = 180

$\implies$ 180 = 180

$~~~~~~~~~$

$~~~~~~~~~~~~~~~~~$ $\dag$ Hence Proved $\large{\bf\green{✓}}$