Question

If a right triangle has its two other angles labeled as 3x + 10 and 5x + 16, find the

Answer 1

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Sum of the interior angles of any triangle equal 180 degrees .

Thus ;

$(3x + 10) + (5x + 16) + 90 = 180$

Subtract sides 90

$(3x + 10) + (5x + 16) + 90 - 90 = 180 - 90$

Simplification

$(3x + 10) + (5x + 16) = 90$

$3x + 10 + 5x + 16 = 90$

Collect like terms

$3x + 5x + 10 + 16 = 90$

$8x + 26 = 90$

Subtract sides 26

$8x + 26 - 26 = 90 - 26$

$8x = 64$

Divide sides by 8

$\frac{8x}{8} = \frac{64}{8}$

$x = 8$

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So ;

The angle marked as 3x + 10 would measure 34° degrees.

$3(8) + 10 = 24 + 10 = 34$

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And ;

The angle marked as 5x + 16 would measure 56° degrees.

$5(8) + 16 = 40 + 16 = 56$

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Done...