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
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)
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°