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Maths-

General

Easy

Question

The points in the figure shown lie in the same plane. If $triangle A B F space i s space c o n g r u e n t space t o space triangle space E D G$ , where $angle A space c o r r e s p o n d s space t o space angle E space a n d space angle B space c o r r e s p o n d s space t o space angle D$ , what is the measure, in degrees, of $angle G C F$ ? (Disregard the degree symbol when gridding your answer.)

The correct answer is: 100°

Given, $straight angle B F A equals 40 to the power of ring operator$ (also same as $straight angle C F G$ )
Given $straight triangle ABF approximately equal to straight triangle EDG$
Step 1:- Find the $straight angle D G E$ using congruence
So, here by congruence $straight angle DGE equals straight angle BFA$
$straight angle D G E equals 40 to the power of ring operator$ ( is also same as $straight angle CGF$ )
Step 2 :- Find $straight angle G C F$ using sum of angle in triangle is 180°
In $straight triangle GCF$ ,
$straight angle CGF plus straight angle CFG plus straight angle GCF equals 180 to the power of ring operator$ (sum of angles in a triangle )
$40 to the power of ring operator plus 40 to the power of ring operator plus straight angle GCF equals 180 to the power of ring operator$
$therefore straight angle GCF equals 100 to the power of ring operator$

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