In the following figure abcd and aefg are two parallelograms. if angle c = 60 then angle gfe is

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9th Standard CBSE

Mathematics

Time : 01:00:00 Hrs

Total Marks : 50

(a)
A square is a rectangle

(b)
A square is a rhombus

(c)
A parallelogram is a trapezium

(d)
A kite is a parallelogram.

2

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In the figure, ABCD and AEFG are parallelograms. If ∠ C = 55∘, what is the measure of ∠ E?

Solution

Given: $∠ C = 55^{\circ}$
In the parallelogram ABCD, we have
$∠ D A B = ∠ D C B . . . . (i)$ (Opposite angles of a parallelogram)
Similarly in parallelogram $∠ G A E = ∠ G F E . . . . (i i)$
From $(i)$ and $(i i),$ we have
$∠ D C B = ∠ G F E = 55^{\circ}$ $(∵ ∠ D C B = ∠ C = 55^{\circ})$ $A E F G,$
Hence $∠ F = 55^{\circ}$

Mathematics
RD Sharma
Standard VIII

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