Question

find the measure of the unknown angle​

Answer 1

Answer:

• 36°.

Step-by-step explanation:

Given:

› AB∥CD

To find:

› ∠p

Construction:

Through O, draw EF∥AB.

Solution:

› Since EF∥AB, AO is a transversal.

∠BAO + ∠AOF = 180°

• [∵ Co-interior angles]

⇒ 59° + ∠AOF = 180°

∴ ∠AOF = 121°

Now,

∠AOF + ∠FOC = 265°

• [∵ Given in figure]

⇒ 121° + ∠FOC = 265°

∴ ∠FOC = 144°

› Since EF∥CD, OC is a transversal.

∠FOC + ∠OCD = 180°

• [∵ Co-interior angles]

⇒ 144° + ∠OCD = 180°

∴ ∠OCD (p) = 36°

∴ The measure of the unknown angle (p) is 36°.