Question

in a right angled triangle one of the acute angles exceeds the other by 20 degree find the measure of the acute angles

Answer 1

Answer:

35

Step-by-step explanation:

Let of acute angle be = x.

let other acute angle be = x - 20

we know that ,

the sum of the angles in a triangle =180

90 + x + ( x - 20 ) =180

90 + 2x -20 = 180

70 + 2x = 180

2x = 180 - 70

2x = 110

x = 110 /2

x = 55.

∴ The one of acute angle  = x

                                          = 55.

∴ the other acute angle = x - 20

                                      = 55 - 20  

                                     =  35.

I hope this helps

Answer 2

Given:

✰ In a right angled triangle, one of the acute angles exceeds the other by 20 degree.

To find:

✠ The measure of both the acute angles.

Solution:

Let's understand the concept first! First we will assume that one acute angle of right angled triangle be x and then the other angel exceeds by 20 degree which means we will add 20° to x and we know there is always one angle in right angled triangle which is 90°. After that we will all the third angles of right angled triangle and we know sum of interior angles of right angled triangle is 180°. Thus, forming equation and doing required calculations, we can find both the acute angles of right angled triangle.

Let's find out...

Let one acute angle of right angled triangle be x°

then the other acute angle = (x + 20)°

Third angle = 90° [ ∵ One angle in right angled triangle

✭ Sum of angles of triangle = 180° ✭

➤ x + x + 20° + 90° = 180°

➤ 2x + 110° = 180°

➤ 2x = 180° - 110°

➤ 2x = 70

➤ x = 70/2

➤ x = 35

∴ One acute angle of right angled triangle = 35°

➤ Other angle = x + 20°

➤ Other angle = 35° + 20°

➤ Other angle = 55°

∴ Other acute angle of right angled triangle = 55°