Two straight lines intersect. One pair of vertically opposite angles is (4x + 5)° and (6x − 15)°. Find the size of the angle marked (4x + 5)°.
Show Worked Solution
Worked Solution
Step 1: Use the vertically opposite angles property.
Vertically opposite angles are equal, so:
4x + 5 = 6x − 15
Step 2: Solve for x.
5 + 15 = 6x − 4x
20 = 2x
x = 10
Step 3: Substitute x = 10 into (4x + 5)°.
Angle = 4(10) + 5 = 40 + 5 = 45°
Check: 6(10) − 15 = 60 − 15 = 45° ✓
Correct answer: 45°
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