Question

In the following figure o is the centre of the circle angle xoy = 40 degree angle twx = 120 degree and xy is parallel to tz find angle xzy ,angle yxz, angle tzy​

Answer 1

Answer:

40°

Step-by-step explanation:

by distance clearance method

Answer 2

In the following figure o is the centre of the circle angle xoy = 40 degree angle twx = 120 degree and xy is parallel to tz.

Consider the figure while going through the following steps.

Construction: Take a point V on the circumference of the circle and join XV and YV.

(i) angle xzy

∠ xoy = 40°   (given)

(angle subtended at the center of the circle is twice the angle subtended at any point on the circumference of the circle)

∴ ∠ xoy = 2 ∠ xvy  

∠ xvy = ∠ xzy  (given figure)

∠ xzy = 1/2 × ∠ xoy = 1/2 × 40°

∴ ∠ xzy = 20°

(ii) angle yxz

∠ xwt + ∠ xwz = 180°  (as these form a straight line)

120° + ∠ xwz = 180°

⇒  ∠ xwz = 180° – 120° = 60°

⇒ ∠ xwz + ∠ xyz  = 180°    (supplementary angles)  

⇒ 60° + ∠ xyz = 180°

⇒ ∠ xyz = 180° – 60° = 120°

∴  In Δ xyz

∠ yxz + ∠ xyz + ∠ xzy = 180°   (∵ sum of the angles of triangle is 180˚)

⇒  ∠ yxz + 120° + 20° = 180°

⇒ ∠ yxz + 140° = 180°

⇒  ∠ yxz = 180° – 140°

∴ ∠ yxz = 40°

(iii) angle tzy​

xy ∥ tz  

∠ xyz + ∠ tzy = 180° (as sum of the consecutive interior angles is 180˚ )

⇒  120° + ∠ tzy = 180°

⇒  ∠ tzy = 180° – 120°

∴ ∠ tzy = 60°