Question

Two lines AB and CD intersect at O. If `∠`AOC + `∠`COB + `∠`BOD = 270°, find the
measures of `∠`AOC, `∠`COB, `∠`BOD and `∠`DOA.

Answer 1

Given: `∠`AOC + `∠`COB + `∠`BOP = 270°

To find: `∠`AOC, `∠`COB, `∠`BOD and `∠`DOA

Here, `∠`AOC + `∠`COB + `∠`BOD + `∠`AOD = 360°              [Complete angle]

⇒  270 + `∠`AOD = 360°

⇒ `∠` AOD = 360° - 270°

⇒ `∠`AOD = 90°

Now,

`∠`AOD + `∠`BOD = 180°                [Linear pair]

90 + `∠`BOD = 180°

⇒ `∠`BOD = 180° - 90°

 ∴ `∠`BOD = 90°

`∠`AOD = `∠`BOC = 90°    [Vertically opposite angles]

`∠`BOD = `∠`AOC = 90°  [Vertically opposite angles]