Mathematics
Find the size of each lettered angle in the following figure:
Rectilinear Figures
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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°.
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