Question

find the angle in the following figure

please help to find these answers​

Answer 1

Answer:

Step-by-step explanation:

i) ∠DAB = 1/2 (160°)

            = 80°

ABPD is a cyclic quadrilateral

∴ ∠DPB = 180°-80°

             =100° (opposite angles of a cyclic quadrilateral are                      supplementary)  

ii) draw XY⊥RS

   ∠PXY=90°

   ∠RYX=90°

  in ΔMXY

∠MXY= 135° - 90°

          = 45°

∠MYX = 90° - 40°

           = 50°

∠XMY = 180°- (45°+50°)

           =180° - 95°

           = 85°

iii) in ΔQRS

  ∠QRT is an external angle

⇒ 65° = 28° + x°

∴ x° = 37°

in ΔPQS

∠PSQ = 180° - (90°+37°)

=180°- 127°

=53°

iv) since ABCD is a ║gm

AB║CD

⇒ DP║AB

⇒∠DPA = ∠PAB (A.I.A)

∴∠DPA = 40°

similarly CP║AB

⇒∠CPB = ∠PBA

⇒ ∠CPB = 80°