Given:
Triangle ABC is right angled at A.
[tex]m\angle B=(5x+7)^\circ[/tex]
[tex]m\angle C=(4x+29)^\circ[/tex]
To find:
The degree measure of each angle in the triangle.
Solution:
According to the given information,
[tex]m\angle A=90^\circ[/tex]
[tex]m\angle B=(5x+7)^\circ[/tex]
[tex]m\angle C=(4x+29)^\circ[/tex]
Now,
[tex]m\angle A+m\angle B+m\angle C=180^\circ[/tex] (Angle sum property)
[tex]90^\circ+(5x+7)^\circ+(4x+29)^\circ=180^\circ[/tex]
[tex](9x+126)^\circ=180^\circ[/tex]
[tex]9x+126=180[/tex]
[tex]9x=180-126[/tex]
[tex]9x=54[/tex]
Divide both sides by 9.
[tex]x=\dfrac{54}{9}[/tex]
[tex]x=6[/tex]
Now,
[tex]m\angle A=90^\circ[/tex]
[tex]m\angle B=(5(6)+7)^\circ[/tex]
[tex]m\angle B=37^\circ[/tex]
[tex]m\angle C=(4(6)+29)^\circ[/tex]
[tex]m\angle C=53^\circ[/tex]
Therefore, the measures of ∠A, ∠B, ∠C are 90°, 37°, 53° respectively.
