Question

please answer by solving​

Answer 1

Answer:

please answer by solving

Step-by-step explanation:

please answer by solving

Answer 2

Step-by-step explanation:

Given :-

In the given figure angle C = 100° and angle D = 50° and the bisectors of angle A and angle B intersect at P.

To find:-

Find the measure of angle APB ?

Solution :-

In the quadrilateral ABCD

The bisectors of angle A and angle B intersect at P.

angle C = 100°

angle D = 50°

We know that

The sum of all angles in a quadrilateral is 360°

=> angle A + angle B + angle C + angle D = 360°

=> angle A + angle B + 100°+50° = 360°

=> angle A + angle B + 150° = 360°

=> angle A + angle B = 360°-150°

=> angle A + angle B = 210°

On dividing by 2 both sides then

=>( angle A + angle B)/2 = 210°/2

=> (angle A + angle B )/2 = 105° -------(1)

In ∆ APB ,

The sum of all angles in a triangle is 180°

=> angle APB+ angle PAB + angle PBA = 180°

=> angle APB+ (angle A)/2 +( angle B)/2 = 180°

Since the bisectors of angle A and angle B intersect at P.

=> angle APB +(angle A+angle B)/2 = 180°

=> angle APB + 105° = 180° ( from (1))

=> angle APB = 180°-105°

=> angle APB = 75°

Answer:-

The measure of an angle APB is 75°

Used formulae:-

• The sum of all angles in a triangle is 180°
• The sum of all angles in a quadrilateral is 360°
• The angle bisector bisects the angle into two equal parts .