Respuesta :
Answer:
The measure of one interior angle is 130°
The measure of other interior angle is 50° .
Step-by-step explanation:
Given as :
The measure of one interior angle of a parallelogram is 30° more than two
times the measure of another angle.
Let The measure of one interior angle = x°
And The measure of other interior angle = y°
∵ Interior angle on same side of transversal are supplementary
So, ∠x + ∠y = 180° .........A
And according to question
∠x = 2×∠y + 30° ...........B
Solving eq A and eq B
2×∠y + 30° + ∠y = 180°
Or, 3×∠y = 180° - 30°
Or, 3×∠y = 150°
∴ ∠y = [tex]\frac{150}{3}[/tex]
i.e ∠y = 50°
So, The measure of other interior angle = ∠y = 50°
Put the value of ∠y in eq B
∵ ∠x = 2×∠y + 30°
Or, ∠x = 2×50° + 30°
Or, ∠x = 100° + 30°
i.e ∠x = 130°
So, The measure of one interior angle = ∠x = 130°
Hence, The measure of one interior angle is 130° and The measure of other interior angle is 50° . Answer
