find the measure of the unknown angle
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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°.
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