Geometry
Two consecutive angles of a parallelogram have measure (x+17) and (4x - 7). What is the measure of the larger angle?
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Facts:
- Two consecutive angles of a parallelogram are supplementary.
- Supplementary angles measures 180°.
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Solve for x.
[tex]\tt \Large (x + 17) + (4x - 7) = 180[/tex]
[tex]\tt \Large x + 17 + 4x - 7 = 180[/tex]
[tex]\tt \Large x + 4x + 17 - 7 = 180[/tex]
[tex]\tt \Large 5x + 10 = 180[/tex]
[tex]\tt \Large 5x = 180 - 10[/tex]
[tex]\tt \Large 5x = 170[/tex]
[tex]\tt \Large 5x \div 5 = 170 \div 5[/tex]
[tex]\tt \Large \blue{x = 34}[/tex]
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Solve for (x + 17)°
[tex]\tt \Large (x + 17)\degree[/tex]
[tex]\tt \Large (34 + 17)\degree[/tex]
[tex]\tt \Large \purple{\bold{51\degree}}[/tex] (smaller angle)
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Solve for (4x - 7)°
[tex]\tt \Large (4x - 7)\degree[/tex]
[tex]\tt \Large (4(34) - 7)\degree[/tex]
[tex]\tt \Large (136 - 7)\degree[/tex]
[tex]\tt \Large \purple{\bold{129\degree}}[/tex] (larger angle)
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Final Answer:
The larger angle measures [tex]\tt \Large \purple{\bold{129\degree}}[/tex].
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