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

In the adjacent figure. AC = 6 cm, AB = 5 cm and angleBAC = 30^(@) . Find the area of the triangle.

triangle ABC and triangle DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see the given figure). If AD is extended to intersect BC at P, show that, ( i ) triangle ABD = triangle ACD (ii) triangle ABP = triangle ACP (iii) AP bisects angle A as well as angle D. (iv) AP is the perpendicular bisector of BC

ABCD is a quadrilateral in which AD = BC and angle DAB = angle CBA (see the given figure). Prove that ( i ) triangle ABD = triangle BAC, ( ii) BD = AC and (iii) angle ABD = angle BAC

In right triangle ABC, right angled at C, M is the midpoint of hypotenuse AB. C is joined to M and produced to a point D such that DM = CM. Point D is joined to point B (see the given figure). Show that: (i) triangle AMC = triangleBMD (ii) angle DBC is a right angle (iii) triangleDBC = triangleACB (iv) CM=1/2 AB

Find the area of sector, whose radius is 7 cm. with the given angle : i. 60^(@) ii. 30^(@) iii. 72^(@) iv. 90^(@) v. 120^(@)

In the given figure an ideal gas changes its state from A to state C by two paths ABC and AC . (i) Find the path along which work done is the least. (ii) The internal energy of gas at A is 10J and amount of heat supplied to change its state to C through the path AC is 200J . Calculate the internal energy at C . (iii) How much is the heat involved in the process ABC and ADC ?

Given two independent events A and B such that P(A) = 0.3, Find (i) P(A and B) (ii) P(A and not B) (iii) P(A or B) (iv) P(neither A nor B)

ABC is a triangle in which altitudes BE and CF to sides AC and AB are equal (see the given figure). Show that ( i ) triangle ABE ~= triangle ACF (ii) AB = AC i.e ABC is an isoceles triangle