Question

if one angle of a parallelogram is 30 degree less than twice the smallest angle then find the measure of each angle

Answer 1

the angle is .... 70, 110, 70, 110

Answer 2

Given:

• One angle of a parallelogram is 30° less than twice the smallest angle.

To Find:

• The measure of each angle

Solution:

• We know that the sum of all the angles of a parallelogram is 360°.
• Draw a parallelogram and name it as ABCD, let ∠A = (2x-30)° (from the given data)
• Opposite to ∠A will the same, so ∠C = (2x-30)°

• Name the angles B and D as 'x' respectively.
• Now add all the given.
• We get, ∠A+∠B+∠C+∠D = 360°
• (2x-30)°+x°+(2x-30)°+x° = 360°
• (2x)°+2x°+2x°-60°=360°
• 6x° = 420°
• x° = 420°/6° = 70°
• Substitue the values of 'x' in the unknown angles.

• We get, ∠A =  (2x-30)° = 2*70°-30
• ∠A = 140°-30° = 110°
• ∠A = ∠C = 110° and ∠B = ∠D = 70°

∴ The angles are 110°,70°,110°, and 70°.