Question

Find the measure of angle L?

Answer 1

`\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies S=180(6-2)\implies S=720 \\\\[-0.35em] ~\dotfill\\\\ (120)+(8x)+(6x-7)+\stackrel{\measuredangle L}{(7x-3)}+(5x)+\stackrel{\measuredangle O}{(90)}=720\implies 26x+200=720 \\\\\\ 26x=520\implies x=\cfrac{520}{26}\implies x=20~\hfill \underset{\measuredangle L}{\stackrel{7(20)~~ - ~~3}{\text{\LARGE 137}}}`

Answer 2

• C. 137

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Sum of interior angles of 6-sides polygon is:

• S = 180(6 - 2) = 180*4 = 720

Set equation for the sum of interior angles and solve for x:

• 120 + 90 + 5x + 7x - 3 + 6x - 7 + 8x = 720
• 200 + 26x = 720
• 26x = 520
• x = 20

Find the measure of angle L:

• 7x - 3 =
• 7*20 - 3 =
• 140 - 3 =
• 137

Correct choice is C.