In figure, ABCD and AEFG are two parallelograms. If ∠C = 55º, determine ∠F.
We have, ABCD and AEFG are two parallelograms and ∠C = 55°. Since, ABCD is a parallelogram, then opposite angles of a parallelogram are equal.
∠A = ∠C = 55° ......(i)
Also, AEFG is a parallelogram.
∴ ∠A = ∠F = 55° .....[From equation (i)]
Concept: Properties of a Parallelogram - Property: The Opposite Sides of a Parallelogram Are of Equal Length.
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In the given figure, ABCD and AEFG are two parallelograms. If ∠C = 58°, find ∠F.
ABCD and AEFG are two parallelograms as shown below:
Since ABCD is a parallelogram, with ∠C = 58°
We know that the opposite angles of a parallelogram are equal.
Therefore,
∠A = ∠C
∠A = 58°
Similarly, AEFG is a parallelogram, with ∠A = 58°
We know that the opposite angles of a parallelogram are equal.
Therefore,
∠F = ∠C
∠F = 58°
Hence, the required measure for ∠F is 58°.
Concept: Another Condition for a Quadrilateral to Be a Parallelogram
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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∘
In the parallelogram ABCD, we have
∠DAB=∠DCB....(i) (Opposite angles of a parallelogram)
Similarly in parallelogram ∠GAE=∠GFE....(ii)
From (i) and (ii), we have
∠DCB=∠GFE=55∘ (∵∠DCB=∠C=55∘)AEFG,
Hence ∠F=55∘
Mathematics
RD Sharma
Standard VIII
24