Question

The largest angle of a triangle is equal to the sum of other two angles the smallest angle is 1/4 of the largest one . find the angles .

Answer 1

1. A=B+C
2. A+B+C=180°
3. A+A=180°
4. 2A=180°
5. A=90°
6. C=1/4 A
7. C=1/4×90°=22.5°
8. B=A-C
9. B=90°-22.5°=67.5°

Answer 2

❥${\underline{\underline{\large{\mathtt{ANSWER:-}}}}}$

Three angles are 90°, 22.5° and 67.5°.

❥${\underline{\underline{\large{\mathtt{EXPLANATION:-}}}}}$

•Given:-

• The largest angle of a triangle is equal to the sum of other two angles.
• The smallest angle is 1/4 of the largest one .

•To find :-

• Angles of the triangle.

• Solution :-

Let the three angles of the triangle be A°, B° and C°.

Consider,

The largest angle = A°

Two others angles = B° and C°

If the measure of the largest angle is equal to the sum of other two angles.

Then largest angle = 180°/2 = 90°

The smallest angle is 1/4 of the largest angle.

Therefore,

Smallest angle = 90°/4 = 22.5°

★ We know the sum of three angles of a triangle is 180° ★

A°+B°+C° = 180°

→ 90°+22.5°+C = 180°

→ C = 67.5°

Hence the largest angle is 90° and the others two angles are 22.5° and 67.5°.