cari nilai sudut APB​

Answer:The measurement of ∠APB=80° Step-by-step explanation:Given:In quadrilateral ABCD ∠C=100° and ∠D=60°  .Now, let ∠PAB=[tex]x[/tex] and ∠PBA=[tex]y[/tex]As, sum of all interior angles of a quadrilateral is 360°.∠A+∠B+∠C+∠D=360°⇒[tex]2x+2y+100+60=360[/tex]     (as the line AP and BP bisect ∠A and ∠B respectively so, ∠A=2x and ∠B=2y)⇒[tex]2x+2y+160=360[/tex]subtracting 160 on both sides⇒[tex]2x+2y=200[/tex]dividing by 2 on both the sides⇒[tex]\frac{2x}{2} +\frac{2y}{2}=\frac{200}{2}[/tex]⇒[tex]x+y=100[/tex]  ........(1)Now, in triangle PAB:Sum of interior angles of triangle is 180°.∠PAB+∠PBA+∠APB=180°Let ∠APB be z.⇒[tex]x+y+z=180[/tex]Putting the value from the above equation (1) ⇒[tex]100+z=180[/tex]Subtracting 100 from both sides⇒[tex]z=80[/tex]⇒ ∠APB=80°Therefore, the measurement of  ∠APB=80° .