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The measure of angle 1 is 71° ⇒ c
Step-by-step explanation:
Look to the attached figure:
∵ Line l intersect line n
∴ Angle 63° and angle (15x - 3) are linear pair
- The sum of the linear pair angles is 180°
∵ 63° + (15x - 3)° = 180°
- Add like terms
∴ 60 + 15x = 180
- Subtract 60 from both sides
∴ 15x = 120
- Divide both sides by 15
∴ x = 8
∵ Line m intersect line n
∴ Angle (8x + 7) and angle 1 are vertical opposite angles
- The vertical opposite angles are equal in measure
∴ m∠1 = 8x + 7
∵ x = 8
- Substitute the value of x to find m∠1
∴ m∠1 = 8(8) + 7
∴ m∠1 = 64 + 7
∴ m∠1 = 71
The measure of angle 1 is 71°
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