Question

theta + phi is ?

a)" "38

b)" "44

c)" "42

d)" "40

Solution

This question can be solved using simple concepts of geometry.

Here theta = angleAED and phi = angleBFC

Also angleBAE= 18 and angleCDE= 22

Since BAF and CDF are straight line.

Hence, angleBAE + angleEAF = 180

=> 18 + angleEAF = 180

=> angleEAF = 180 - 18

=> angleEAF = 162

Similarly,

angleCDE + angleEDF = 180

=> 22 + angleEDF = 180

=> angleEDF = 180 - 22

=> angleEDF = 158

We know that sum of angles of quadilateral is 360.

Hence in quadilateral AEDF,

theta + phi + angleEAF + angleEDF = 360

=> theta + phi + 162 + 158 = 360

=> theta + phi = 360 - (162 + 158)

=> theta + phi = 360 - 320

=> theta + phi = 40