The measure of the angle is 50°.
When the sum of two angles measures up to 180° then these angles are known as supplementary angles of each other.
for example, ∠x + ∠y = 180°, therefore, the ∠x and ∠y are the supplementary angles of each other.
When the sum of two angles measures up to 90° then these angles are known as complementary angles of each other.
for example, ∠x + ∠y = 90°, therefore, the ∠x and ∠y are the complementary angles of each other.
Let's assume that the angle is x.
The supplementary angle of x is (180°-x).
The complementary angle of x is (90°-x).
According to the question,
(180°-x) = 4(90°-x)-30°,
(180°-x) = 4(90°-x)-30°
180 - x = 360 - 4x - 30
4x - x = 360 - 30 -180
3x = 150
x = 50°
Hence, the measure of the angle is 50°.
Learn more about Supplementary and Complementary angles:
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