Find the size of each lettered angle in the following figure:

Question

KnowledgeBoat · Accepted Answer

Here, AB || CD and BC || AD So, ABCD is a || gm y = ∠ABC (As opposite angles of || gm are equal) y = 2∠ABD (As diagonals bisect vertex angle so BD bisects ∠ABC) y = 2 x 53° = 106° Also, y + ∠DAB = 180° (DC || AB, sum of co-int ∠s = 180°) ∠DAB = 180° – 106° = 74°. Thus, x = ∠DAB [As AC bisects ∠DAB] ⇒ x = x 74° = 37° and ∠DAC = x = 37° Also, z = ∠DAC = 37° [Alternate angles are equal] Hence, x = 37°, y = 106° and z = 37°.

Mathematics

Find the size of each lettered angle in the following figure:

Rectilinear Figures

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