Find the measure of the given angles. Show work!!

Question

asked Apr 26, 2022 235k views

1 Answer

Pikaling · Answer 1 · 2022-04-30T10:11:10+0000

Given:

The figure of a right angle triangle.

To find:

The value of x and measures of all angles of the triangle.

Solution:

According to the angle sum property, the sum of all interior angles of a triangle is 180 degrees.

Using angle sum property, we get

$(x+60)^\circ+(x+50)^\circ+90^\circ=180^\circ$

$(2x+200)^\circ=180^\circ$

$(2x)^\circ=180^\circ-200^\circ$

$(2x)^\circ=-20^\circ$

It can be written as

(2x)=-20

Divide both sides by 2.

x=-10

The value of x is -10.

Now,

$m\angle A=x+50$

$m\angle A=-10+50$

$m\angle A=40$

And,

$m\angle B=x+60$

$m\angle B=-10+60$

$m\angle B=50$

Therefore, the value of x is -10, measure of angle A is 40 degrees and measure of angle B is 50 degrees.