Question

If one of the angle of a triangle is 65° and the other two angles are in the ratio 2:3.Find the other two angles​

Answer 1

Given

• One angle of a triangle is 65°
• Two angles are in the ratio 2:3

_________________________________

To Find

• The other two angles.

_________________________________

Solution

Angle 1 ⇒ 65°

Since the other two angles are in the ratio 2:3 we can consider angle 2 and angle 3 as,

Angle 2 ⇒ 2x

Angle 3 ⇒ 3x

We know that the sum of the interior angles in a triangle is 180°. So we will solve this equation to find the unknown angles ⇒ 65 + 2x + 3x = 180

Let's solve your equation step-by-step.

65 + 2x + 3x = 180

Step 1: Simplify the equation.

⇒ 65 + 2x + 3x = 180

⇒ 65 + 5x = 180

Step 2: Subtract 65 from both sides of the equation.

⇒ 5x + 65 - 65 = 180 - 65

⇒ 5x = 115

Step 3: Divide 5 from both sides of the equation.

⇒ 5x ÷ 5 = 115 ÷ 5

⇒ x = 23

∴ Angle 1 ⇒ 65°

∴ Angle 2 ⇒ 2x ⇒ 2(23) ⇒ 46°

∴ Angle 3 ⇒ 3x ⇒ 3(23) ⇒ 69°

∴ The two unknown angles are of measures 46° and 69°

_________________________________

Answer 2

Answer:

Other two angles are 46° and 69°

Step-by-step explanation:

GivEn:

• One angle of triangle = 65°
• Other two angles of triangle are 2:3

To finD:

• Value of other two angles.

Explanation:

Let suppose that the other two angles are 2x and 3x respectively.

Now,

According to the given question:

65°+2x+3x = 180° ———(angle sum property of triangle)*

=> 65°+5x = 180°

=> 5x = 180°-65°

=> 5x = 115°

=> x = $\small{\bf{ \frac{115}{5} }}$

=> x = 23

Now, we found that the value of x is 23

Measures of two other angles are as:

First angle:

2x = 2×23 = 46°

Second angle:

3x = 3×23 = 69°

More information :

When we were doing solution of our question then we have used a word - "Angle sum property of triangle".

Let us know about "Angle sum property of triangle" :

Angle sum property of triangle : Angle sum property of triangle state that, sum of all interior angle of a triangle is 180°.