Q155 of 160 Page 144

In parallelogram MODE, the bisector of ∠M and O meet at Q. Find the measure of ∠MQO.

Let MODE be the parallelogram and Q be the point of intersection of the bisector of ∠M and ∠O

The figure is attached below:

Now, in a parallelogram, the adjacent angles are supplementary.

∴ ∠EMO + ∠DOM = 180°

⇒ 1/2 (∠EMO + ∠DOM) = 1/2 180°

⇒ 1/2∠EMO + 1/2∠DOM = 1/2 180°

∠QMO + ∠QOM = 90°

Now, in ΔMOQ,

∠QMO + ∠QOM + ∠MQO = 180⁰

⇒ 90⁰ + ∠MQO = 180⁰

⇒ ∠MQO = 90⁰

153

In parallelogram LOST, SN Ol and SM LT. Find STM, SON and NSM.

154

In trapezium HARE. EP and RP are bisectors of E and R respectively. find ∠HAR and ∠EHA.

156

A playground is in the form of a rectangular ATEF, two players are standing at the points of F and B where EF = EB. Find the values of x and y.

157

In the following figure of a ship. ABDH and CEFG are two parallelograms. Find the value of x.