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Recall that two angles are complementary if the sum of their measures is 90. Find the measures of two complementary angles if one angle is more than times the other angle. An angle that measures y degrees is formed by 2 rays with the same start point. The first ray rises vertically, and the second ray rises from left to right. A second angle that measures x degrees is formed by 2 other rays with the same start point. The first ray rises from left to right and the second ray extends horizontally to the right. The smaller angle measures nothing

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MrRoyal

Question:

Recall that two angles are complementary if the sum of their measures is 90degrees. Find the measures of two complementary angles if one angle is 6 degrees more than two times the other angle?

Answer:

The angles are: 28 and 62 degrees respectively

Step-by-step explanation:

Let the two angles be x and y where the bigger angle is x.

So, we have:

[tex]x + y = 90[/tex] ---- Complementary angles

[tex]x = 6 + 2y[/tex] --- Given

Required

Find x and y

Substitute [tex]x = 6 + 2y[/tex] in the first equation

[tex]x + y = 90[/tex]

[tex]6 + 2y +y= 90[/tex]

[tex]6 + 3y= 90[/tex]

Solve for 3y

[tex]3y= 90 -6[/tex]

[tex]3y= 84[/tex]

Solve for y

[tex]y= 84/3[/tex]

[tex]y= 28[/tex]

Recall that: [tex]x = 6 + 2y[/tex]

[tex]x = 6 + 2 * 28[/tex]

[tex]x = 6 + 56[/tex]

[tex]x = 62[/tex]

So, the angles are: 28 and 62 degrees respectively

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