Part (a)
Step-by-step Explanation:
As ∠K is a right angle.
i.e.
also
Equation to find x
As we know that The angle sum of a Triangle is 180°.
so
m∠K + m∠L + m∠M = 180°
[tex]90\:+\:\left(2x+19\right)\:+\:\left(3x+19\right)\:=\:180[/tex]
[tex]90+2x+19+3x+19=180[/tex]
[tex]5x+90+19+19=180[/tex]
[tex]5x+128=180[/tex]
[tex]5x=52[/tex]
[tex]x=\frac{52}{5}[/tex]
Part (b)
Step-by-step Explanation:
Finding the degree measures of each angle.
As
As ∠K is a right angle.
so
Putting [tex]x=\frac{52}{5}[/tex] in m∠L = (2x+19)°
m∠L = (2x+19)°
= [tex]2\left(\frac{52}{5}\right)+19[/tex]
[tex]=\frac{199}{5}[/tex]
[tex]=39.8[/tex]
so
m∠L = 39.8°
Putting [tex]x=\frac{52}{5}[/tex] in m∠M = (3x+21)°
m∠M = (3x+21)°
[tex]=3\left(\frac{52}{5}\right)+19[/tex]
[tex]=\frac{251}{5}[/tex]
[tex]=50.2[/tex]
so
m∠M = 50.2°
Verification:
m∠K + m∠L + m∠M = 180°
90° + 39.8° + 50.2° = 180°
90° + 90° = 180° ∵ 39.8° + 50.2° = 90°
180° = 180°
