Answer:
The measure of ∠2 is 150° ⇒ last answer
Step-by-step explanation:
In a parallelogram:
- Each two opposite angles are equal in measures
- Each to adjacent angles are supplementary (their sum is 180°)
In the parallelogram
∵ ∠1 and ∠3 are opposite angles
∴ m∠1 = m∠3
∵ m∠1 = 3 x + 15
∵ m∠3 = 7 x - 5
- Equate them
∴ 7 x - 5 = 3 x + 15
- Subtract 3 x from both sides
∴ 4 x - 5 = 15
- Add 5 to both sides
∴ 4 x = 20
- Divide both sides by 4
∴ x = 5
Substitute the value of x in ∠1 or ∠3 to find their measure
∵ m∠1 = 3(5) + 15
∴ m∠1 = 15 + 15
∴ m∠1 = 30°
∵∠1 and ∠2 are adjacent angles
∴ m∠1 + m∠2 = 180°
- Substitute m∠1 in the equation
∴ 30 + m∠2 = 180
- Subtract 30 from both sides
∴ m∠2 = 150°
