Question

In a right angled triangle , one of the acute angle exceeds the other by 20°,find the measure of both the acute angles in the right angled triangle

Answer 1

ATQ, in a right angled triangle, one of the acute angle exceeds the other by 20°

let the smaller acute angle be x°

therefore the greater one is x + 20°

now we've got all three angles of the right angle triangle :-

» 90°(since it's a right angle triangle)

» x° and x + 20°

we know that sum of all angles in a triangle = 180°

➡ 90° + x° + x + 20° = 180°

➡ 110° + 2x = 180°

➡ 2x = 180 - 110

➡ 2x = 70°

➡ x = 70/2

➡ x = 35°

hence, the angles are :-

• smaller acute angle = x = 35°

• greater acute angle = x + 20 = 55°

verification :-

= 35° + 55° + 90°

= 90° + 90°

= 180°

Answer 2

Answer:

Step-by-step explanation:

Given :-

One of the acute angle exceeds the other by 20°.

To Find :-

The measure of both the acute angles.

Formula to be used :-

Angle Sum property of Triangle.

a + b + c = 180°

Solution :-

In a right angled triangle, there is one angle of 90°

let one of acute angle be x.

let other angle be  x + 20

Putting all the values, we get

⇒ a + b + c = 180°

⇒ 90 + x + x + 20 = 180

⇒ 2x + 110 = 180

⇒ 2x = 180 - 110

⇒ 2x = 70

⇒ x = 70/2

⇒ x = 35

The 1st angle is x°

= 35°

The 2nd angle is (x + 20)°

= 35 + 20

= 55°

Hence, the measure of both the acute angles is  90°, 35° and 55°.