Question

AD is a diameter of circle ABCDE . Angle BAC=22° & angle ADC=60°. AE and ED are parallel lines. Find the values of w, x,y,and z

Answer 1

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Answer 2

Given: D = diameter, angle BAC=22, angle ADC = 60, AE and ED are parallel lines.

To find: values of x, y, z, w.

Solution:

(lets mark centre ad O)

• Now, since AD is diameter,

• In triangle ACD,

              ang A+ ang C + ang D = 180

              w+90 + 60 = 180

(if diameter is one of the side of a triangle, then the triangle is right angle triangle)

• So,

               w=30.

• Now, 22 + w = z ........(alternate interior angles)

                22 + 30 = z

                z = 52.

• Now, lets do a construction, join AE,

• So ang ABE = ang ADE ......(angle subtended by a chord is equal)

                  x + y = 52   ........(alternate interior angles)

• Now in triangle EOD,

                   ang E + ang D + ang O = 180

                  angle O = 76

                  ang EAD = 76/2= 38  =  ang ECD

• (angle subtended by a chord is equal)

• Now in triangle ECD,

               ang E + ang C + ang D = 180

               y + 60+ 52+ 38 = 180

               y = 30

• Now, x + y = 52

               x= 52 - y

               x= 22

Answer:

• Hence, x= 22, y = 30, z = 52, w=30.