# Find measure of the angle or arc indicated help?

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- Engr. RonaldLv 72 months ago
21x - 2 + 38x + 5 = 180

59x + 3 = 180

59x = 180 - 3

59x = 177

x = 3

then

21x - 2 = 21(3) - 2 = 61 ° x 2 = 122°

38x + 5 = 38(3) + 5 = 119°

mFGH = 360 - 122 = 238 ° answer//

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- PuzzlingLv 72 months ago
When the 4 points of a quadrilateral are on a circle, the opposite angles are supplementary (add to 180°)

21x - 2 + 38x + 5 = 180

59x + 3 = 180

59x = 177

x = 177/59

x = 3

From that we can figure out angle FAH:

38(3) + 5

= 114 + 5

= 119°

And the subtended arc FGH would be twice as much.

arc FGH = 2 * 119° = 238°

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