Question

In Fig. 74, if AB || CO, ∠CAB = 49°, ∠CBD = 27° and∠BDC = 112°, then the values of x and y are
(a) x = 41, y = 90
(b) x = 41,y = 63
(c) x = 63, y = 41
(d) x = 90, y = 41

Answer 1

Since, AB || CD
∠ABD + ∠CDB = 180° [Angles on the same side of a transversal line are supplementary]
⇒ x° + 27° + 112° = 180°
⇒ x° = 41°
⇒ x = 41
Now, In △ABC
∠A + ∠B + ∠C = 180° [Angle sum property of triangle]
⇒ 49° + 41°+ y° = 180°
⇒ y° = 90°
⇒ y = 90
Hence, the correct answer is option (a).