Question

Can somebody help me?

Answer 1

Part (a)

Step-by-step Explanation:

As ∠K is  a right angle.

i.e.

• m∠K = 90°

also

• m∠L = (2x+19)°

• m∠M = (3x+21)°

Equation to find x

As we know that The angle sum of a Triangle is 180°.

so

m∠K + m∠L + m∠M = 180°

$90\:+\:\left(2x+19\right)\:+\:\left(3x+19\right)\:=\:180$

$90+2x+19+3x+19=180$

$5x+90+19+19=180$

$5x+128=180$

$5x=52$

$x=\frac{52}{5}$

Part (b)

Step-by-step Explanation:

Finding the degree measures of each angle.

As

As ∠K is  a right angle.

so

• m∠K = 90°

Putting $x=\frac{52}{5}$ in m∠L = (2x+19)°

m∠L = (2x+19)°

         = $2\left(\frac{52}{5}\right)+19$

         $=\frac{199}{5}$

         $=39.8$

so

m∠L = 39.8°

Putting $x=\frac{52}{5}$ in m∠M = (3x+21)°

m∠M = (3x+21)°

         $=3\left(\frac{52}{5}\right)+19$

          $=\frac{251}{5}$

          $=50.2$

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°