Five rays are drawn from a point O on a straight line MN, creating four angles on the same side of the line. The angles are (3p + 5)°, 40°, (2p − 5)°, and 25°. Find the value of the angle (3p + 5)°.
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Worked Solution
Step 1: All angles on a straight line sum to 180°.
(3p + 5) + 40 + (2p − 5) + 25 = 180
Step 2: Collect like terms.
5p + 65 = 180
Step 3: Solve for p.
5p = 180 − 65 = 115
p = 23
Step 4: Find the required angle.
(3p + 5)° = 3(23) + 5 = 69 + 5 = 74°
Check: 74 + 40 + (2(23) − 5) + 25 = 74 + 40 + 41 + 25 = 180° ✓
Answer: 74°
Answer: 74°
Correct answer: 74°
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