Q100 of 113 Page 128

In Fig. 5.53, find the value of ∠BOC, if points A, O and B are collinear.

∠ AOD, ∠ DOC and ∠ COB are linear pairs.

So the sum of this three angles is 180⁰

(x-10) + (4x-25) + (x + 5) = 180

⇒ 6x = 180 + 30

⇒ 6x = 210

⇒ x = 35⁰

∠BOC = (x + 5)⁰ = 40⁰

Measures (in degrees) of two supplementary angles are consecutive odd integers. Find the angles.

In Fig. 5.52, AE || GF || BD, AB || CG || DF and ∠CHE = 120°. Find ∠ABC and ∠CDE.

101

In Fig. 5.54, if l ||m, find the values of a and b.

102

In Fig. 5.55, l ||m and a line t intersects these lines at P and Q, respectively. Find the sum 2a + b.