The three angles of a quadrilateral are in the ratio 2:5:7.The sum of the greatest and smallest among these angles is 180. What is the measure of the fourth angle?
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Answer:
116°
Step-by-step explanation:
Angles of Quadrilateral = 2:5:7
Sum of Angles of Quadrilateral = 360°
2x + 5x + 7x = 360°
14x = 360°
x = 360°/14
x = 25.71°
Now,
2x = 2 × 25.71°
= 51.42°
5x = 5 × 25.71°
= 128.55°
7x = 7 × 25.71°
= 179.97°
Now, Fourth Angle = 360° - (51.42° + 128.55° + 179.97°)
= 360° - 244°
= 116°
Therefore, The measure of Fourth Angle of Quadrilateral is 116°.
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