The measure of one angle is seven times the measure of its complement. Find the measure of the smaller angle. ( pls if u answer the question show me how).

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  11.25°

Step-by-step explanation:

Let s represent the smaller angle. Complementary angles have a sum of 90°, so we have ...

  s + 7s = 90°

  8s = 90° . . . . . collect terms

  s = 11.25° . . . . . divide both sides by 8

The smaller angle is 11.25°.

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Check

The larger angle is 7(11.25°) = 78.75°.

11.25° +78.75° = 90° . . . . as required

11.25 degrees

Step-by-step explanation:

Two complementary angles are angles that both add to 90deg.

x = angle 1

y = complementary angle

x = 7×y

And

x + y = 90deg

So

7×y + y = 90deg

8×y = 90deg

y = 90deg / 8

y = 11.25deg

((And x = 78.75deg, but they don't ask for that.))

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

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step-by-step explanation:

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