Question

7. Each of the two equal angles of a triangle is twice the third angle. Find the angles of the triangle​

Answer 1

Answer:

1st Angle = 72°

2nd Angle = 72°

3rd Angle = 36°

Step-by-step explanation:

In the triangle

Let us consider the third angle to be x

3rd Angle = x

2nd Angle = 2x   (The angle is double the third angle)

1st Angle = 2nd Angle   (Given)

1st Angle = 2x

According to angle sum property of triangle

(1st Angle) + (2nd Angle) + (3rd Angle) = 180°

2x + 2x + x = 180°

5x = 180°

x = 180° ÷ 5

x = 36°

1st Angle = 2x ⇒ 2 x 36° ⇒ 72°

2nd Angle = 2x ⇒ 2 x 36° ⇒ 72°

3rd Angle = x ⇒ 36°

Hope this answer helps you.

Answer 2

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{GIVEN:-}$

Each of the two equal angles of a triangle is twice the third angle.

$\underline \mathbb{TO \: FIND:-}$

All the angles of the triangle.

$\underline \mathbb{ASSUMPTION:-}$

Let, the third angle of the triangle be x.

$\therefore$ the second angle of the triangle is 2x

So, the first angle of the triangle is also 2x

$\underline \mathbb{FORMULA:-}$

Sum of all the 3 angles of triangle = 180°

$\underline \mathbb{BY \: THE \: PROBLEM:-}$

$x + 2x + 2x = 180 \degree \\ \\ \implies \: 5x = 180 \degree \\ \\ \implies \:x = \cancel\frac{180 \degree}{5} \\ \\ \implies \:x = 36 \degree$

$\underline \mathbb{ANSWER:-}$

The third angle of the triangle = x = 36°

The second angle of the triangle = 2x = (2 × 36)°= 72°

The first angle of the triangle = 2x = (2 × 36)°= 72°

$\underline \mathbb{VERIFICATION:-}$

$1st \: angle +2nd \: angle +3rd \: angle = 180 \degree \\ \\ \implies \: 36 \degree + 72 \degree + 72 \degree = 180 \degree(proved)$