Question

PARALLELOGRAM QUESTION LOTS OF POINTS, SERIOUS ANSWERS ONLY I WILL REPORT

Answer 1

Consecutive angles of a parallelogram are supplementary

• 7x+21+5x+15=180
• 12x+36=180
• 12x=144
• x=12

<C:-

• 5(12)+15
• 60+15
• 75°

Answer 2

m∠C = 75°

Explanation:

Theorem:

The consecutive angles of a parallelogram are supplementary (sum to 180°).

⇒ m∠D + m∠E = 180°

⇒ (7x + 21) + (15 + 5x) = 180

⇒ 7x + 21 + 15 + 5x = 180

⇒ 12x + 36 = 180

⇒ 12x = 144

⇒ x = 12

Theorem:

Opposite angles of a parallelogram are equal.

⇒ m∠C = m∠E

⇒ m∠C = 15 + 5x

Substituting found value of x:

⇒ m∠C = 15 + 5(12)

⇒ m∠C = 75°