Question

line segments AB and CD intersect at O such that AC parallel DB. If angle CAB = 35 degree and angle CDB = 55 degree , then angle BOD =​

Answer 1

Step-by-step explanation:

We know that AC parallel to BD and AB cuts AC and BD at A and B, respectively. ∠CAB = ∠DBA (Alternate interior angles) ∠DBA = 35° We also know that the sum of all three angles of a triangle is 180°. Hence, for △OBD, we can say that: ∠DBO + ∠ODB + ∠BOD = 180° 35° + 55° + ∠BOD = 180° (∠DBO = ∠DBA and ∠ODB = ∠CDB) ∠BOD = 180° – 90° ∠BOD = 90°