Question

ABCD is a parallelogram and angle A=80°. Find other angles of a parallelogram.​

Answer 1

• Measure of angle B is 100°.
• Measure of angle C is 80°
• Measure of angle D is 100°.

Step-by-step explanation:

Given:-

• ABCD is a parallelogram and ∠A is 80°.

To find:-

• Other angles of parallelogram.

Solution:-

Opposite sides of parallelogram are equal and parallel.

AB || DC and AD is a transversal.

We know that,

Sum of two adjacent interior angles when two parallel lines intersect by an transversal is 180°. We also call this statement as Co-interior angles.

So,

➝ ∠A + ∠B = 180°

➝ 80° + ∠B = 180°

➝ ∠B = 180° - 80°

➝ ∠B = 100°

We also know that,

Opposite angles of parallelogram are equal.

So,

➝ ∠A = ∠C = 80°

➝ ∠B = ∠D = 100°

Therefore,

Angles of parallelogram ABCD are

∠B = 100°

∠C = 80°

∠D = 100°

Answer 2

Answer:

Given :-

• ABCD is a parallelogram and ∠A = 80° .

To Find :-

• What is the other angles of a parallelogram.

Solution :-

ABCD is a parallelogram, and ∠A = 80°

So, we know that,

➢ AB || DC

⇒ ∠A + ∠D = 180 [ Co - interior angle ]

⇒ 80° + ∠D = 180°

⇒ ∠D = 180° - 80°

➠ ∠D = 100°

And, also we know that,

⇒ ∠A = ∠C = 80° [ Adjacent angle ]

And, ∠D = ∠B = 100° [ Adjacent angle ]

Hence, the required angles of parallelogram are,

✦ ∠D = 100°

✦ ∠C = 80°

✦ ∠B = 100°

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