Question

An Angle measures 64 more than the measure of its supplementary angle what is the measure of each angle

Answer 1

Original angle = 122*

Supplementary angle = 58*

Explanation:

A supplementary angle is one of two angles that make up 180*

If one angle is 30*, its supplementary angle is 150*. 30 + 150 = 180.

So in this case we have two angles, the original and the supplementary angle. The original angle is 64* more than the supplementary angle. The key word is MORE.

The formula to figure it out would look like this: x + (x + 64) = 180

x is the supplementary angle

x + 64 is the original angle (64 MORE than its supplementary angle)

180 is the total measure of the two angles because they are supplementary and we know that supplementary angles always equals 180* when added together.

Take the formula and do a little algebra.

x + (x + 64) = 180

Subtract 64 from both sides

x + x = 116

Combine the x's

2x = 116

Divide both side by 2

x = 58

Remeber we know that the original angle is 64 more than the supplementary angle, so we'll add the 64 to the value of x and we get 122.

x + 64 = 122

Check our work:

x + (x + 64) = 180

58 + 58 + 64 = 180

Answer 2

Given :

• An angle which measures 64° more the measure of its supplementary angle.

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To Find :

• The measure of its supplementary angle.

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Solution :

• Let's assume the one of the supplementary angle as x and the other angle as (x + 64)° .

Now,

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According to the Question :

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`\longrightarrow\qquad \sf{{x + (x + 64) {}^( \circ) = {180}^( \circ) }}`

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`\longrightarrow\qquad \sf{{x + x + 64 {}^( \circ) = {180}^( \circ) }}`

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`\longrightarrow\qquad \sf{{2x + 64 {}^( \circ) = {180}^( \circ) }}`

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`\longrightarrow\qquad \sf{{2x = {180}^( \circ) - 64 {}^( \circ)}}`

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`\longrightarrow\qquad \sf{{2x = {116}^( \circ) }}`

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`\longrightarrow\qquad \sf{{x = \frac{{116}^( \circ)}{2} }}`

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`\longrightarrow\qquad \mathfrak{\pmb{{x = {58}^( \circ) }}}`

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Therefore,

• One angle = 58°
• Other angle = 58° + 64° = 122°

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Henceforth ,

• The measure of the two angles are 122° and 58° .