GCE Mathematics 2022 Objective — Question 27
Question 27 of 50 from the General Certificate of Education (GCE) Mathematics 2022 Objective paper, with the correct answer and a full explanation.
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In the diagram, MRW and MNST are straight lines. |MN|=|NR|, angle MNR=110 degrees and angle WRS=86 degrees. Find the value of x.
- A. 86 degrees
- B. 70 degrees
- C. 51 degreesCorrect
- D. 42 degrees
Explanation
Since |MN|=|NR|, base angles of isosceles triangle MNR are equal: RMN = MRN = y. y+y+110=180, so 2y=70, y=35 degrees. Considering line MRW: y + angle NRS + 86 = 180, so NRS = 180-35-86 = 59 degrees. In triangle SNR: x + RNS + NRS = 180, so x = 180-70-59 = 51 degrees.
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