Q17 of 33 Page 108

In the square ABCD, M is a point on extended portion of DA so that ∠CMD = 30°. The diagonal BD intersects CM at the point P. Let us write the value of ∠DPC.


In the given figure, Given a square ABCD, M is a point on extended portion of DA so that ∠CMD = 30°. The diagonal BD intersects CM at the point P


To find: ∠DPC


∠CDA = 90° [All angles of a square are 90°]


Also,


∠MDC + ∠CDA = 180° [Linear pair]


⇒ ∠MDC = 90°


Now, BD is diagonal and diagonal of a square bisect the angles



In ΔDPM, By angle sum property


∠CMD + ∠PDM + ∠DPC = 180°


⇒ 30° + ∠CDM + ∠CDB + ∠DPC = 180°


⇒ 30° + 90° + 45° + ∠DPC = 180°


⇒ ∠DPC = 15°


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