Question

measure of one angle of a parellogram is 100⁰ find the other three angles​

Answer 1

Answer:

If Parallelogram has 4 angles such that ∠A,B,C and D

∠A is 100°

Opposite angles are always equal in Parallelogram

And Adjacent angles are Supplimentary (Means: They sum up to 180°)

opposite of ∠A is ∠C so ∠A = ∠C = 100°

∠A and ∠B are Adjacent angles

so ∠A + ∠B = 180°

100° + ∠B = 180°

∠B = 180° - 100° = 80°

∠B = ∠D because they are opposite

Hence ∠D = 80°

∴ If One angle that is ∠A is 100° then other 3 angles that are ∠B, ∠C and ∠D are 80°, 100° and 80° Respectively.

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Answer 2

Given: One angle of a parallelogram is $100$⁰.

We have to find the other three angles of a parallelogram.

As we know that the opposite angles of a parallelogram are equal.

And Adjacent angles are Supplementary (Means: They sum up to $180$°)

$\therefore$ If one angle is $100$° then the angle opposite to it would be

Now let the other two angles be $x$ and$x.$

So,

$=>100+x+x+100=360\\=>2x+200=360\\=>2x=360-200\\=>2x=160\\=>x=\frac{160}{2} \\\\=>x=80$

$\therefore$The other two angles will be $80$° each

Hence, the other three angles of the parallelogram will be $80$°, $100$°, $80$°.