Question

In the parallelogram, <1=3x+15 and <3=7x-5. Find the measure of <2.

30 degrees
20 degrees
140 degrees
150 degrees

Answer 1

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°