Answered

One angle of a parallelogram measures 20 what are the measures of the other three angles in the parallelogram

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Answer:

  • 160°, 20° and 160°

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Step-by-step explanation:

Let us assume A, B, C and D are the four angles of the parallelogram. Where, ∠A = 20° and we have to find the measure of ∠B, ∠C and ∠D

So, If ∠A = 20°, then So, also ∠C = 20°.

  • [Opposite angles of a parallelogram are equal to each other]

Therefore,

  • The measure of ∠C is 20°

⠀

And, ∠A and ∠B are adjacent angles. We know,

  • Sum of two adjacent angles = 180°

So,

⇒ ∠A + ∠B = 180°

⇒ 20° + ∠B = 180°

⇒ ∠B = 180° – 20°

⇒ ∠B = 160°

So,

  • The measure of ∠B = 160°

⠀

So, If ∠B = 160°, then So, also ∠D = 160°.

  • [Opposite angles of a parallelogram are equal to each other]

Therefore,

  • The measure of ∠D is 160°
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