In the given diagram the value of x is equal to
Correct answer: C. 65°
- A. 35°
- B. 45°
- C. 65°
- D. 75°
Explanation
65° is correct. It satisfies the angle relationships in the diagram.The two slanted lines meet above the horizontal line, forming a triangle whose top angle is x. The angle labelled 125∘ at the left is outside that triangle, so the triangle's left base angle is its supplement:left base angle=180∘−125∘=55∘right base angle=60∘ Sum of triangle angles = 180∘ sotop angle of the triangle =180∘−(55∘+60∘)=180∘−115∘=65∘Now, angle x and the top angle of the triangle are vertically opposite angles therefore they are equal.x = 65∘Options 35°, 45°, and 75° are incorrect because they do not adhere to the angle sum properties of the shape as indicated in the diagram.
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About Quantitative Reasoning
Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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