Question

angel C of a triangle ABC is the sum of the other two angels A and B . if the ratio of angel A and angel B is 3:2 , find the measure of all the three angels​

Answer 1

Answer :

The three angles are 54°, 36°, and 90°

Step-by-step explanation:

Step 1 : Let's assume angles of the △ABC as :

➪ ∠B = $3x$

➪ ∠A = $2x$

Given,

→ ∠A + ∠B = ∠C

So,

→ ∠C = $3x + 2x = \boldsymbol 5x$

Step 2 : Find the value of $x$ :

Using the angle sum property of a △

The sum of three angles of a △is equal to 180°

So we can say that,

$\implies \bf \angle A + \angle B + \angle C = 180 \degree$

Where,

• ∠A = $3x$
• ∠B = $2x$
• ∠C = $5x$

So,

$\implies 3x + 2x + 5x = 180 \degree$

$\implies 10x = 180 \degree$

$\implies x = \dfrac{180}{10} \degree$

$\implies x = 18 \degree$

$\therefore x = \bf 18 \degree$

Step 3 : Calculate the three angles :

Therefore, the three angles are :

➪ ∠A = $3x = \bf 3(18) = 54 \degree$

➪ ∠B = $2x = \bf 2(18) = 36 \degree$

➪ ∠C = $5x = \bf 5(18) = 90 \degree$

Check point :

Three angles we have is 54°, 36° and 90°

According to the angle sum property of a triangle it must be equal to 180°

Let's check,

→ 54° + 36° + 90°

→ 90° + 90°

→ 180°

Clearly, we are getting 180°

Hence, proved ${\boxed{\green{\checkmark{}}}}$