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In figure, X = 62°, LXYZ = 54°. If YO and ZO are the bisectors of LXYZ and L}{ZY respectively of Ll XYZ, find LOZ¥ and LYOZ. .Az

In figure, X = 62°, LXYZ = 54°. If YO and ZO are the bisectors of LXYZ and L}{ZY respectively of Ll XYZ, find LOZ¥ and LYOZ.
.Az

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
8 months ago
In . LX + LXYZ + LYZX = 180° [Angle sum property] ::) 62° + 54° + LYZX = 180° ::) LYZX = 180° - 116° = 64° ...(i) Also, LYZX = 2LOZV [•: OZ is bisector of LYZX] ::) 2LQzy = 64° ::) LOZV = 32° ...(ii) [From (i)] Also, LOyz = .!.LXYZ = .!. x 54° = 27° ...(iii) 2 2 [OY is bisector of .LXYZ] In oyz, LOyz + Lozy + LYOZ = 180° [Sum of angles of a triangle is 180°.] ::) 27° + 32° + LYOZ = 180° ::) LYOZ = 180° - 59° = 121° Thus, LOZV = 32° and LYOZ = 121°.

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