In the given figure, `angleX = 62^(@), angleXYZ = 54^(@)`. In `DeltaXYZ ` If YO and ZO are the bisectors of `angleXYZ` and `angleXZY` respectively find `angleOZY` and `angleYOZ`

In the given figure angleA= 40^(@) . If bar(BO) and bar(CO) are the bisectors of angleB and angleC respectively. Find the measure of angleBOC .

In the adjacent figure ray OS stands on a line PQ. Ray OR and ray OT are angle bisectors of anglePOS and angleSOQ respectively. Find angleROT .

In the adjoining figure, BX and CY are the bisectors of angle ABC and angle ACB respectively. If AB=AC and BY=4 cm, then find the lengths of AX.

It is given that angleXYZ= 64^(@) and XY is produced to point P. A ray YQ bisects angleZYP . Draw a figure from the given information. Find angleXYQ and reflex angleQYP .

In the given figure sides QP and RQ of ΔPQR are produced to points S and T respectively. If angleSPR = 135^(@) and anglePQT = 110^(@) , find anglePRQ.

In the figures given below AB || CD. EF is the transversal intersecting AB and CD at G and H respectively. Find the values of x and y. Give reasons

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta) y(t)x'(t)dt, S=int_(alpha)^(beta) x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. If the curve given by parametric equation x=t-t^(3), y=1-t^(4) forms a loop for all values of t in [-1,1] then the area of the loop is