Question

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

measure of each angle.
The angle marked as 3x + 10 would measure
I
degrees.
The angle marked as 5x + 16 would measure
degrees.

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

`(8x)/(8) = (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...