Given: ∆abc, ab = cb bd − altitude to ac p ∈ bd, pb = pc m∠abc = 48° find: m∠pcd

The measure of angle PCD is 42 degree.

Explanation:

It is given that in ∆ABC,

AB = CB  

BD − altitude to AC

P ∈ BD, PB = PC

∠ABC = 48°

Since the AB and CB are equal therefore by property of isosceles triangle the angle BAC and angel BCA are equal.

According to the angle sum property the the sum of interior angles of a triangle is 180.

The altitude BD on AC divides the angle b in two equal parts because triangle ABC is an isosceles triangle.

Since PB=PC , so triangle BPC is an isosceles triangle.

From the figure it is noticed that,

Therefore, the measure of angle PCD is 42 degree.

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