Discussion
P is a point on line AB and PQ is a ray such that ∠ QPA = 7x and ∠ QPB = 5x. Then, the value of (8x - 10°) is :
Answer: B
The value is 110°.
Since P lies on the line AB, angles QPA and QPB form a linear pair and add up to 180°:
\[ \begin{aligned} 7x + 5x &= 180^\circ \\ x &= 15^\circ \\ 8x - 10^\circ &= 120^\circ - 10^\circ = 110^\circ \end{aligned} \]
118° and 102° come from adding or subtracting the wrong amount, and 140° uses x = 18.75°, which would follow only if the angles added up to 225°.
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