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°
    Instraight 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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