In the adjoining figure abcd and aefg are two parallelograms. if ∠c = 55ᵒ, then, find ∠f.

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: $\angle C={55}^{\circ }$

In the parallelogram ABCD, we have​

$\angle DAB=\angle DCB....\left(i\right)$ (Opposite angles of a parallelogram)​

Similarly in parallelogram $\angle GAE=\angle GFE....\left(ii\right)$

​ From $\left(i\right)$ and $\left(ii\right),$​ we have

$\angle DCB=\angle GFE={55}^{\circ }$ $(\because \angle DCB=\angle C={55}^{\circ })$AEFG,​

Hence $\angle F={55}^{\circ }$

Mathematics

RD Sharma

Standard VIII