Question

24) In figure, 2X = 62°, ZXYZ = 54°, if YO and Zo are the bisectors of ZXYZ and 2XZY,
respectively of AXYZ, find LOZY and LYOZ.​

Answer 1

Answer:

In the given figure, ∠X = 62° and ∠XYZ = 54° ∠XYZ + ∠XZY + ∠YXZ = 180° …(i) [Angle sum property of a triangle] ⇒ 54° + ∠XZY + 62° = 180° ⇒ ∠XZY + 116° = 180° ⇒ ∠XZY = 180° – 116° = 64° Now, ∠OZY = 1/ 2 × ∠XZY [∵ZO is bisector of ∠XZY] = 1 /2 × 64° = 32° Similarly, ∠OYZ = 1/2 × 54° = 27° Now, in ∆OYZ, we have ∠OYZ + ∠OZY + ∠YOZ = 180° Angle sum property of a triangle] ⇒ 27° + 32° + ∠YOZ = 180° ⇒ ∠YOZ = 180° – 59° = 121° Hence, ∠OZY = 32° and ∠YOZ = 121Read more on Sarthaks.com - https://www.sarthaks.com/11966/the-figure-62-xyz-54-and-are-the-bisectors-xyz-and-xzy-respectively-xyz-find-ozy-and-yoz