Q154 of 160 Page 144

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

Adjacent angles along a side of a trapezium are supplementary.

Hence, ∠R + ∠A = 180 ________(i)

Similarly, ∠E + ∠H = 180 ________(ii)

According to given data in question,

The complete ∠R = 2×30 = 60

And ∠E = 2×25 = 50

Because, EP and RP are bisectors of E and R respectively.

By Eq (i) and (ii),

∠A = 180-60 = 120

∠H = 180-50 = 130

152

A rectangular MORE, is shown below:

Answer the following questions by giving appropriate reason.

(i) Is RE = OM? (ii) Is MYO = RXE?

(iii) Is MOY = REX? (iv) Is ∆MYO = ∆RXE?

(v) Is MY = RX?

153

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

155

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

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.