Question

Value of the angle x is 64° and work out the value of angle y for this triangle

Answer 1

Answer:

In ∆XYZ, we have

∠XYZ+∠XZY+∠X=180°    (Sum of three angles of a triangle =180°)

⇒540+∠XZY+62°=180°

⇒∠XZY=180°−54°−62°=64°

It is given that OY and OZ are bisectors of ∠XYZ and ∠XZY respectively

Therefore, ∠OZY=1/2(∠XZY)

=1/2(64°)

=32°

Similarly, ∠OYZ=1/2(∠XYZ)  

=1/2(54°)  

=27  

In ∆OYZ, we have

∠OYZ+∠OZY+∠YOZ=180°  (Sum of three angles of a triangle =180°)

⇒27°+32°+∠YOZ=18°

⇒∠YOZ=180°−27°−32°=121°

Therefore, ∠OZY=32° and ∠YOZ=121°

Step-by-step explanation:

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