In the adjacent figure- the bisectors of angle A and angle B meet in a point P-If angle C-100-circ and angle D-60-circ Find the measure of angle APB-

Question

In the adjacent figure- the bisectors of angle A and angle B meet in a point P-If  angle C-100-circ  and angle D-60-circ Find the measure of angle APB-

Toppr Admin · Accepted Answer

60-x2218-100-x2218-x2220-A-x2220-B-360-x2218-x21D2-x2220-A-x2220-B-200-x2218-x21D2-x2220-A-x2220-B2-100-x2218-x21D2-x2220-BAP-x2220-ABP-100-x2218-But-xA0- -x2220-BAP-x2220-ABP-x2220-APB-180-x2218-x21D2-x2220-APB-80-x2218-

In the adjacent figure, the bisectors of $∠ A$ and $∠ B$ meet in a point P.If $∠ C = 100^{\circ}$ and $∠ D = 60^{\circ}$ Find the measure of $∠ A P B$ .

$60^{\circ} + 100^{\circ} + ∠ A + ∠ B = 360^{\circ}$
$\Rightarrow ∠ A + ∠ B = 200^{\circ}$
$\Rightarrow \frac{∠ A + ∠ B}{2} = 100^{\circ}$
$\Rightarrow ∠ B A P + ∠ A B P = 100^{\circ}$
But $∠ B A P + ∠ A B P + ∠ A P B = 180^{\circ}$
$\Rightarrow ∠ A P B = 80^{\circ}$

In the adjacent figure, the bisectors of ∠A and ∠B meet in a point P.If ∠C=100∘ and ∠D=60∘ Find the measure of ∠APB.

60∘+100∘+∠A+∠B=360∘⇒∠A+∠B=200∘⇒∠A+∠B2=100∘⇒∠BAP+∠ABP=100∘But ∠BAP+∠ABP+∠APB=180∘⇒∠APB=80∘

In the adjacent figure, the bisectors of $∠ A$ and $∠ B$ meet in a point P.If $∠ C = 100^{\circ}$ and $∠ D = 60^{\circ}$ Find the measure of $∠ A P B$ .

$60^{\circ} + 100^{\circ} + ∠ A + ∠ B = 360^{\circ}$
$\Rightarrow ∠ A + ∠ B = 200^{\circ}$
$\Rightarrow \frac{∠ A + ∠ B}{2} = 100^{\circ}$
$\Rightarrow ∠ B A P + ∠ A B P = 100^{\circ}$
But $∠ B A P + ∠ A B P + ∠ A P B = 180^{\circ}$
$\Rightarrow ∠ A P B = 80^{\circ}$