Question

Adjacent angles of a parallelogram are (x-30°) and (x+50°). Find all the angles of the parallelogram. Please give the answer step by step.​

Answer 1

Answer :

• The angles of the parallelogram are 50⁰,80⁰ and 130⁰

Given :

• Adjacent angles of a parallelogram are (x - 30⁰) and (x + 50⁰)

To find :

• Angles of the parallelogram

Solution :

Given,

• x - 30⁰
• x + 50⁰

↦ x - 30⁰ + x + 50⁰

Adjacent angles of a parallelogram are supplementary so,

↦ x - 30⁰ + x + 50⁰ = 180⁰

↦ 2x - 20⁰ = 180⁰

↦ 2x = 180⁰ - 20⁰

↦ 2x = 160

↦ x = 160/2

↦ x = 80⁰

Now , we have to find the angles of the parallelogram :

↦ x - 30⁰

↦ 80 - 30

↦ 50

↦ x + 50

↦ 80 + 50

↦ 130⁰

Hence , The angles of the parallelogram are 50⁰ , 80⁰ 130⁰

Verification :

↦ x - 30⁰ + x + 50⁰ = 180⁰

↦ 80 - 30 + 80 + 50 = 180

↦ 50 + 130 = 180⁰

↦ 180⁰ = 180⁰

Hence , Verified