Mathematics: Can somebody help me?

Step-by-step explanation:then the answer is 5...

Can somebody help me? - id5674645, vadrian4739

Ответ:

jashaikamatuteowwp1p

22.01.2022

Mathematics

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°.

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 ∠K is a right angle.

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

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

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°

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