Question

The measure of an angle of a parallelogram is 70degrees.find the measure of remaining angles​

Answer 1

The sum of the angles of a parallelogram is 360 degrees. At least two angles will be the same unless one angle is of measure 90 degrees (in which case all four are 90). Hence, the remaining angles are 70 degrees and 2 110 degree angles.

Answer 2

✪ Question ✪

The measure of an angle of a parallelogram is 70°. Find the measure of remaining angles.

✪ Given ✪

The measure of an angle of a parallelogram is 70°.

✪ To find ✪

The measure of remaining angles.

✪ Solution ✪

Let ABCD be the parallelogram, where ∠B = 70°.

As we know that the sum of the adjacent angles of a parallelogram is 180°, we can say-

∠A + ∠B = 180°

↝∠A + 70° = 180°

↝∠A = (180 - 70)°

↝∠A = 110°

Since, the opposite angles of a parallelogram are equal, we can say-

• ∠A = ∠C = 110°
• ∠B = ∠D = 70°

✪ Hence ✪

• ∠A = 110°
• ∠B = 70°
• ∠C = 110°
• ∠A = 70°

✪ Therefore ✪

The measure of the remaining angles of the parallelogram are 110°, 70° and 110°.

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✪ Verification ✪

The sum of all angles of a parallelogram is 360°.

So,

∠A + ∠B + ∠C + ∠D = 360

↝110 + 70 + 110 + 70 = 360

↝180 + 180 = 360

↝360 = 360

So, L.H.S = R.H.S.

Hence, verified.

๑ Hope this helps you. ๑