Question

Find angle K of this problem

Answer 1

m∠K = 55°

Solution:

Given JKLM is a isosceles trapezoid.

Measure of ∠M = (11x – 18)° and Measure of ∠K = (3x + 16)°

In a isosceles trapezoid opposite angles are supplementary.

⇒ m ∠M + m ∠K = 180°

⇒ (11x – 18)° + (3x + 16)° = 180°

⇒ 11x° – 18° + 3x° + 16° = 180°

Combine like terms together.

⇒ 11x° + 3x° + 16° – 18° = 180°

⇒ 14°x – 2° = 180°

⇒ 14°x = 180° + 2°

⇒ 14°x = 182°

⇒ x = 13°

Substitute x = 13° in m ∠K.

⇒ m∠K = 3(13°) + 16°

⇒ m∠K = 39° + 16°

⇒ m∠K = 55°

Hence m∠K = 55°.