Answer:
a.[tex]x=10 \textdegree[/tex]
b.
[tex]m\angle L=39\textdegree\\\\m\angle M=51\textdegree\\\\m\angle K=90\textdegree[/tex]
Step-by-step 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;
[tex]180=\perp\angle+(2x+19)+(3x+21)\\\\180=90+(2x+19)+(3x+21)\\\\90=5x+40\\\\5x=50\\\\x=10\textdegree[/tex]
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:
[tex]m\angle L=(2x+19)\textdegree\\\\=(2\times 10+19)\textdegree\\\\=39\textdegree\\\\m\angle M=(3x+21)\textdegree\\\\=(3\times 10+21)\textdegree\\\\=51\textdegree[/tex]
Since, the m∠K is a right angle, it measures 90°
