Question

Figure ABCD is a parallelogram.

Parallelogram A B C D is shown. Angle B is (3 n + 20) degrees and angle D is (6 n minus 25) degrees.

What are the measures of angles B and C?

∠B = 15°; ∠C = 165°
∠B = 65°; ∠C = 115°
∠B = 65°; ∠C = 65°
∠B = 15°; ∠C = 15°

Answer 1

m∠B = 65°, m∠C = 115°

Explanation:

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Answer 2

m∠B = 65°, m∠C = 115°

Solution:

The image of the problem is attached below.

Given ABCD is a parallelogram.

∠B = (3n + 20)° and ∠D = (6n – 25)°

In a parallelogram, opposite angles are equal.

⇒ ∠B = ∠D

⇒ (3n + 20)° = (6n – 25)°

⇒ 3n° + 20° = 6n° – 25°

Combine like terms together.

⇒ 25° + 20° = 6n° – 3n°

⇒ 45° = 3n°

⇒ n = 15°

Substitute n = 15° in ∠B.

⇒ m∠B = 3(15) + 20°

⇒ m∠B = 45° + 20°

⇒ m∠B = 65°

∠B and ∠C are adjacent angles in a figure.

Sum of the adjacent angles in a parallelogram = 180°

⇒ m∠B + m∠C = 180°

⇒ 65° + m∠C = 180°

⇒ m∠C = 180° – 65°

⇒ m∠C = 115°

Hence m∠B = 65°, m∠C = 115°.