Answer:
Hence, ∠ABP=10°
Step-by-step explanation:
We are given that:
AB and CD are tangents of the circle.
Now we are given that m∠ACP=10°.
Also we are given that AP and CP are radius of the given circle that means length of AP and CP are equal.
Also we know that angle opposite to the equal sides are equal that means:
∠ACP=∠PAC.
Hence , ∠PAC=10°.
Also in a triangle the sum of all the angles is 180°.
i.e. ∠ACP+∠PAC+∠APC=180°
this means that 10+10+∠APC=180°
∠APC=180-20
∠APC=180-20=160°
As AB and CD are tangents to the circles that means:
∠BAP=∠BCP=90°
Also APCB is a quadrilateral and we know that sum of all the angles of a quadrilateral=360°
Hence,
∠BAP+∠BCP+∠APC+∠ABC=360°
⇒ 90+90+160+∠ABC=360
⇒ 180+160+∠ABC=360
⇒ 340+∠ABC=360
⇒ ∠ABC=360-340=20°
also ∠ABP=(1/2)∠ABC
Hence, ∠ABP=(1/2)×20°=10°
Hence, ∠ABP=10°
