find the angles measure x,of the following figure 30°,70°,60°,X,
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Given: A geometric figure containing the following angles: 30°, 70°, 60° and x.
To find: The measure of x
Solution: First we need to find all the unknown angles inside the pentagon except x.
As such, the supplementary angle of 60° = (180 - 60)° = 120°.
The supplementary angle of 70° = (180 - 70)° = 110°.
We know that the total sum of all the angles of a pentagon is 540°.
Therefore according to the given figure,
30° + x + x + 120° + 110° = 540°
⇒ 2x + 260° = 540°
⇒ 2x = 540° - 260°
⇒ 2x = 280°
⇒ x = 140°
Hence, the measure of x in the given figure is 140°.
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