In the adjacent figure, it is given that, BC || DE, `angleBAC = 35^(@)` and `angleBCE = 102^(@)` . Find the measure of (i) `angleBCA (ii) `angleADE` and (iii) `angleCED`.

In the adjacent figure, it is given that AB =AC, angleBAC = 36^(@) , angleADB = 45^(@) and angleAEC = 40^(@) . Find (i) angleABC (ii) angleACB (iii) angleDAB (iv) angleEAC .

In the adjacent figure, AB || QR, angleBAQ = 142^(@) and angleABP = 100^(@) . Find (i) angleAPB (ii) angleAQR "and (iii)" angleQRP

In the given figure if AB || DE, angleBAC = 35^(@) and angleCDE = 53^(@) , find angleDCE.

In the given figure ,AB,BC and AC touch the circle at L,M and N respectively .If angleB=70^(@) and angleC=60^(@) ,then the measure of angleLON is :

In the adjacent figure, ABC is a triangle in which angleB = 50^(@) and angleC = 70^(@) . Sides AB and AC are produced. If ‘z’ is the measure of the angle between the bisectors of the exterior angles so formed, then find 'z'.

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 given figure AB || CD, BC || DE then find the values of x and y

ABCD is a quadrilateral in which AD=BC and angleDAB = angleCBA . Prove that: (i) triangleABD ~= triangleBAC (ii) BD = AC (iii) angleABD = angleBAC