If in the figure a || b and c || d, then name the angles that are congruent to (i) `angle1 (ii) angle2`.

In the adjoining figure, line PR touches the circle at point Q . Using the information given in the diagram, answer the following questions. (i) What is the sum of angleTAQ and angleTSQ ? (ii) Write names of angles congruent to angleAQP . (iii) Write names of angles congruent to angleQTS . (iv) If angleTAS= 65^@ , then find angleTQS and arc TS . (v) It angleAQR=42^(@) and angleSQR=58^(@) , then find angleATS .

In the figure ,if angle PAB = 120^@ then angle BPT = …………..

In the adjacent figure BE bot DA and CD bot DA then prove that m angle1 ~= m angle3 .

List the adjacent angles in the given figure.

Find the angle A in triangle ABC, if angle B=60^∘ and angle c=70^∘

Procedure : (i) Draw a circle of many radius with centre O. (ii) Mark any four points A,B,C and D on the boundary. Make a cyclic quadrilateral ABCD and name the angles as in Fig. 1 (iii) Make a replica of the cyclic quadrilateral ABCD with the help of tracing paper (iv) Make the cutout of the angles A,B,C and D as in Fig. 2 (v) Paste the angle cutout angle1,angle2,angle3 and angle4 adjacent to the angles opposite to A,B,C and D as in Fig . 3 Measure the angles angle1+angle3 , and angle2+angle4 . Observe the Fig. 3 and complete the following : {:((i),angleA+angleC= . . . . . . . ,(ii),angleB+angleD =. . . . . . .),((iii),angleC+angleA= . . . . . . .,(iv),angleD+angleB= . . . . . . .):} 2. Sum of opposite angles of a cyclic quadrilateral is . . . . . . . . 3. The opposite angles of a cyclic quadrilateral is . . . . . . .

If the sines of the angles A and B of a triangle ABC satisfy the equation c^2x^2-c(a+b)x+a b=0 , then the triangle a)acute angled b)right angled c)obtuse angled d) sinA+cosA = ((a+b))/c