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julia-pushkina [17]
3 years ago
9

Two angles form a linear pair. The measure of one angle is 24º more than the measure of the other angle. Find the measure of eac

h angle.
Mathematics
1 answer:
Lina20 [59]3 years ago
6 0

Answer:

The measures of the two angles are 78° and 102°

Step-by-step explanation:

<em>When two lines intersects at a point, then pairs of linear angles are formed</em>

  • The linear pair of angles are adjacent angles the sum of their measures is 180°

∵ The two angles form a linear pair

∴ The sum of the two angles = 180°

∵ The measure of one of them = 24° more than the measure

    of the other angle

→ Assume that the smaller one is x, then the greater one is

   x + 24, add them up and equate their sum by 180°

∵ x + x + 24 = 180

→ Add the like term in the left side

∴ 2x + 24 = 180

→ Subtract 24 from both sides

∴ 2x + 24 - 24 = 180 - 24

∴ 2x = 156

→ Divide both sides by 2

∴ 2x/2 = 156/2

∴ x = 78°

∴ The smaller angle = 78°

∵ The larger angle is x + 24

∴ The larger angle = 78 + 24 = 102°

The measures of the two angles are 78° and 102°

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The difference of two supplemtary angles is 58 degrees. Find the measures of the angles
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Answer:

The measure of the angles are 61° and 119°

Step-by-step explanation:

Let the first angle = x°

let the second angle = y°

The sum of two supplementary angles = 180°

x° + y° = 180° ----- equation (1)

based on the given question; "the difference of two supplementary angles is 58 degrees."

x° - y° = 58° ------- equation (2)

from equation (2), x° = 58° + y°

Substitute the value of x into equation (1)

(58° + y°) + y° = 180°

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Thus, the measure of the angles are 61° and 119°

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3 years ago
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