Question

In a given fig. ABCD is a parallelogram, find 2 angle ABC - angle ADC.​

Answer 1

Step-by-step explanation:

ANGLE. ADC=70°

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Answer 2

Given,

In the given figure, ABCD is a parallelogram.

Angle BCE = 70°

To find,

The measure of 2(Angle ABC) - (Angle ADC).

Solution,

We can simply solve this mathematical problem using the following process:

Geometrically,

The opposite sides of a parallelogram are parallel and equal.

{Statement-1}

If two parallel lines have a transversal, then;

a) corresponding angles are equal

b) alternate opposite angles are equal

{Statement-2}

Now, according to the statement-1 and the figure;

In the parallelogram ABCD,

AB||CD (BC is the transversal) and AD||BC (DE is the transversal)

{Statement-3}

Now, according to all the statements;

AB||CD (BC is the transversal)

=> Angle ABC = Angle BCE = 70° (alternate opposite angles)

{Equation-1}

And, AD||BC (DE is the transversal)

=> Angle ADC = Angle BCE = 70° (corresponding angles)

{Equation-2}

Now,

The measure of 2(Angle ABC) - (Angle ADC)

= 2(70°) - (70°)

{according to equation-1 and equation-2}

= 140° - 70°

= 70°

Hence, the measure of 2(Angle ABC) - (Angle ADC) is equal to 70°.