Answer:
x = 14
Step-by-step 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°
