Question

if O is the center of the circle, angle QPR=70 and m(arc PYR) = 160, find
m(arc QXR)
angle QOR
angle PQR​

Answer 1

For angle QPR=70, m(arc PYR) =160,

m(arc QXR) = 140, angle QOR=140, angle PQR = 80.

• Given,
• ∠QPR =70°
• m(arc PYR)= 160
• formula,
• ∠ = 1/2 m(arc PYR)
• Now,
• m(arc QXR)
• ∠QPR = 1/2 m( arc QXR)
• 70 = 1/2 m( arc QXR)
• ∴m( arc QXR) =140°
• Now,
• ∠QOR
• using the properties of triangle, we have,
• ∠QOR=2∠QPR
• =2*70
• =140°
• Now,
• ∠PQR
• ∠PQR = 1/2 m(arc PYR)
• =1/2 * 160
• =80°