Question

The measure of one of the adjacent angles of the parallelogram exceeds
the other by 30°. Find the measure of each angle of parallelogram.​

Answer 1

Answer:

75⁰,105⁰,75⁰,105⁰

Step-by-step explanation:

In parallelograms, Opposite angles are equal and adjacent angles are supplementary

here, angle 1 is 30⁰ more than its adjacent angle

let them be x and y respectively

x = y+30⁰(given)

y + x = 180⁰(supplementary angles)

or y + y + 30⁰ = 180⁰

2y = 180⁰-30⁰

2y = 150⁰

y = 75⁰

if, y = 75⁰, then x = 75⁰ + 30⁰ = 105⁰

The angle opposite to x would be equal to 105⁰

and the angle opposite to y would be equal to 75⁰

therefore, angles = 75⁰, 105⁰, 75⁰, 105⁰