Q8 of 153 Page 166

The supplement of an angle is six times its complement. The measure of this angle is

Let x be the angle then,
complement = 90 – x
supplement = 180 – x

According to question,
180 – x = 6(90 – x)
180 – x = 540 – 6x
180 + 5x = 540
5x = 360
x = 72^O

In the given figure, ACB is a straight line and CD is a line segment such that ∠ACD = (3x – 5)° and ∠BCD = (2x + 10)°. Then, x = ?

In the given figure, AOB is a straight line. If ∠AOC = 40°, ∠COD = 4x° and ∠BOD = 3xׄ°, then x = ?

In the given figure, AB || CD || EF. If ∠ABC = 85°, ∠BCE = x° and ∠CEF = 130°, then x = ?

In the given figure, AB || CD, ∠BAD = 30° and ∠ECD = 50°. Find ∠CED.