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NeX [460]
3 years ago
5

What are the remaining angle measures if the figure is to be a parallelogram?

Mathematics
1 answer:
Kobotan [32]3 years ago
7 0

Answer:

We conclude that:

m∠B = 101°

m∠C = 79°

m∠D = 101°

Step-by-step explanation:

Given the parallelogram ABCD

We know that a parallelogram has opposite angles that are congruent.

Here,

The angles ∠A and ∠C are opposite angles.

Thus,

  • ∠A = ∠C

The angles ∠B and ∠D are opposite angles.

Thus,

  • ∠B = ∠D

<u>Determining the measure of angles of a parallelogram:</u>

As

∠A = 79°

We know

  • ∠A = ∠C

Thus, the measure of the angle ∠C is:

m∠C = 79°

We know that the sum of the measure of two consecutive angles is 180°.

As ∠A and ∠D are consecutive angles, so

∠A + ∠D = 180°

substituting ∠A = 79° in the equation

79° + ∠D = 180°

subtracting 79° from both sides

79° + ∠D - 79° = 180° - 79°

∠D = 101°

Thus, the measure of the angle D is:

m∠D = 101°

We know that the angles ∠B and ∠D are opposite angles.

Thus,

  • ∠B = ∠D

so if m∠D = 101° then ∠B is also 101°.

Therefore, the measure of angle B is:

m∠B = 101°

Hence, we conclude that:

m∠B = 101°

m∠C = 79°

m∠D = 101°

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Answer:

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Answer:

  7.  29 cm

  8.  equation: 61 = (x) +(2x -7) +(3x +2); sides 11, 15, 35

Step-by-step explanation:

7. Let w represent the width. The length is 3 less than twice the width, so the length is 2w-3. The perimeter is given by the formula ...

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8. The equation that should be used is the one that relates the side lengths to the perimeter.

  P = a + b + c . . . . for sides a, b, c

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<em>Comment on problem 8</em>

You will notice that the side lengths do not satisfy the triangle inequality: the sum of the short sides is not greater than the long side. <em>These side lengths cannot form a triangle</em>. Cute algebra, but <em>bad geometry</em>.

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length =88cm

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