Question

Can somebody help me, please?

Answer 1

a.
`x=10 \textdegree`

b.

`m\angle L=39\textdegree\\\\m\angle M=51\textdegree\\\\m\angle K=90\textdegree`

Explanation:

a. We know that angles in a triangle add up to 180°.

-The right angle triangle in the right triangle has a measure of 90°.

We can therefore equate our angles to 180° and solve for x;

`180=\perp\angle+(2x+19)+(3x+21)\\\\180=90+(2x+19)+(3x+21)\\\\90=5x+40\\\\5x=50\\\\x=10\textdegree`

Hence, the angle measure is x=10°

b. Having calculated the value of x from a above as x=10°, we can substitute to find the measures of the two acute angles:

`m\angle L=(2x+19)\textdegree\\\\=(2* 10+19)\textdegree\\\\=39\textdegree\\\\m\angle M=(3x+21)\textdegree\\\\=(3* 10+21)\textdegree\\\\=51\textdegree`

Since, the m∠K is a right angle, it measures 90°