Basic geometry question: Circle

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!!

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