Question

In the triangle below, with right angle A, suppose that m is Angle B=(5x+7) and m is Angle C=(4x+29) Find the degree measure of each angle in the triangle. A= 90 B=(5x+7) C=(4x+29)

Answer 1

(6×-5)°× (×+9)°w(4×)°y

Answer 2

Given:

Triangle ABC is right angled at A.

`m\angle B=(5x+7)^\circ`

`m\angle C=(4x+29)^\circ`

To find:

The degree measure of each angle in the triangle.

Solution:

According to the given information,

`m\angle A=90^\circ`

`m\angle B=(5x+7)^\circ`

`m\angle C=(4x+29)^\circ`

Now,

`m\angle A+m\angle B+m\angle C=180^\circ` (Angle sum property)

`90^\circ+(5x+7)^\circ+(4x+29)^\circ=180^\circ`

`(9x+126)^\circ=180^\circ`

`9x+126=180`

`9x=180-126`

`9x=54`

Divide both sides by 9.

`x=(54)/(9)`

`x=6`

Now,

`m\angle A=90^\circ`

`m\angle B=(5(6)+7)^\circ`

`m\angle B=37^\circ`

`m\angle C=(4(6)+29)^\circ`

`m\angle C=53^\circ`

Therefore, the measures of ∠A, ∠B, ∠C are 90°, 37°, 53° respectively.