Question

In the figure BP = AP = PC then find ∠A

Answer 1

Answer:

∠ABP=100

∘

or 30

∘

Step-by-step explanation:

Given: AB=AC and BP=PC

Join AP

Now, In △ABP and △APC

AB=AC (Given)

BP=PC (Given)

AP=AP (Common)

Thus, △ABP≅△ACP

Hence, ∠BAP=∠CAP=

2

1

∠A=25

∘

∠ABP=∠ACP

In Case I,

∠ABP=

2

1

∠P=55

∘

In Case II,

∠ABP=

2

1

(ext.∠P)=125

∘

Now, In △APB

Sum of angles = 180

∠ABP+∠APB+∠PAB=180

In case I,

∠ABP+25+55=180

∠ABP=100

∘

In case II,

∠ABP+25+125=180

∠ABP=30

∘

therefore, ∠ABP=100

∘

or30

∘

Answer 2

Answer:

<A = 45

because of

<a +<b + <c = 180.

<p =90

<a =45

<b =45