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+…

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asked Jul 20, 2022 88.0k views

2 Answers

Ernist Isabekov · Answer 1 · 2022-07-25T05:55:31+0000

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.