Question

Let triangle ABC have vertices on a circle. Let AD be the altitude and AP be the diameter of the circle. If angle ABC =84 and angle BCA=60 then angle DAP equals to

Answer 1

$\angle DAP=24^{\circ}$

Step-by-step explanation:

In triangle ABC

Angle ABC=84 degrees

Angle BCA=60 degrees

In triangle ABD

$\angle ABD+\angle ADB+\angle BAD=180$degrees

By using triangle angles sum property

Substitute the values then we get

$84+90+\angle BAD=180$

$174+\angle BAC=180$

$\angle BAC=180-174=6^{\circ}$

$\angle ADC=90^{\circ}$

AD is perpendicular to BC

Angle ACP=90 degrees

Because angle subtended at half circle=90 degrees

$\angle BCP=\angle ACP-\angle BAC=90-60=30^{\circ}$

Angle subtended by the same arc at the circumference are equal.

$\angle BAP=\angle BCP$

$\angle BAP=30^{\circ}$

$\angle DAP=\angle BAP-\angle BAD=30-6=24^{\circ}$

$\angle DAP=24^{\circ}$

#Learns more:

https://brainly.in/question/788031 Answered by mysticd

Answer 2

Step-by-step explanation:

here you go thank you