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In AOPQ, m/O = (2x − 5)°, mZP = (3x − 8)°, and mZQ = (10x – 17)º.

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What is the value of x?

User Regular Jo
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1 Answer

3 votes

Answer:

x = 14

Explanation:

You want the value of x in ∆OPQ, where ∠O = (2x − 5)°, ∠P = (3x − 8)°, and ∠Q = (10x – 17)º.

Angle sum theorem

The angle sum theorem tells you the sum of angles in a triangle is 180°. This means ...

∠O +∠P +∠Q = 180°

(2x -5)° +(3x -8)° +(10x -17)° = 180° . . . . . use the given expressions

15x -30 = 180 . . . . . . divide by °, collect terms

x -2 = 12 . . . . . . . . . divide by 15

x = 14 . . . . . . . . . . add 2

The value of x is 14.

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Additional comment

The measures of the angles are ...

O = 23°, P = 34°, Q = 123°

User James Morcom
by
4.2k points