Math, asked by tinutomjohn, 8 months ago

One of the angles of a triangle is 65° and the other angles are in the ratio 2:3. Find the measure of the other two angles.

Answers

Answered by BloomingBud
13

Given:

One angle of a triangle is 65°.

The other angles are in the ratio 2:3

To be found:

The measure of the other two angles.

Here are steps to find the answer-

  • Taking the other two angles as 2x° and 3x°.
  • By angle sum property, sum of all three angles of the triangle is 180°.
  • Then 'x' value will be found.
  • And find the other two angles 2x° and 3x° by putting the value of x.

SOLUTION:

Let the other two angles be 2x° and 3x°

Now,

⇒ 65 + 2x + 3x = 180

[∵ Angle sum property of triangle - Sum of all three interior angles of a triangle is 180°]

⇒ 65 + 5x = 180

⇒ 5x = 180 - 65

⇒ 5x = 115

⇒ x = 115 ÷ 5

⇒ x = 23

The value of x = 23.

Hence,

Other angles are

2x = 2 × 23 = 46°

3x = 3 × 23 = 69°

Verification;

65° + 46° + 69° = 180°

(verified)

Answered by ANANDH1576
0

Answer:

Yep

Step-by-step explanation:

⇒ 65 + 2x + 3x = 180

[∵ Angle sum property of triangle - Sum of all three interior angles of a triangle is 180°]

⇒ 65 + 5x = 180

⇒ 5x = 180 - 65

⇒ 5x = 115

⇒ x = 115 ÷ 5

⇒ x = 23

∴ The value of x = 23.

Hence,

Other angles are

2x = 2 × 23 = 46°

3x = 3 × 23 = 69°

 

65° + 46° + 69° = 180°

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