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Sum of the interior angles of any triangle equal 180 degrees .
Thus ;
[tex](3x + 10) + (5x + 16) + 90 = 180 \\ [/tex]
Subtract sides 90
[tex](3x + 10) + (5x + 16) + 90 - 90 = 180 - 90 \\ [/tex]
Simplification
[tex](3x + 10) + (5x + 16) = 90[/tex]
[tex]3x + 10 + 5x + 16 = 90[/tex]
Collect like terms
[tex]3x + 5x + 10 + 16 = 90[/tex]
[tex]8x + 26 = 90[/tex]
Subtract sides 26
[tex]8x + 26 - 26 = 90 - 26[/tex]
[tex]8x = 64[/tex]
Divide sides by 8
[tex] \frac{8x}{8} = \frac{64}{8} \\ [/tex]
[tex]x = 8[/tex]
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So ;
The angle marked as 3x + 10 would measure 34° degrees.
[tex]3(8) + 10 = 24 + 10 = 34[/tex]
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And ;
The angle marked as 5x + 16 would measure 56° degrees.
[tex]5(8) + 16 = 40 + 16 = 56[/tex]
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Done...
