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Math  /  Geometry

Question(Español)
Two angles are complementary. The measure of one angle is 9∘9^{\circ} more than twice the measure of the other angle. Find the measure of each angle.
Part 1 of 2
The measure of the smaller angle is □\square .
Part 2 of 2
The measure of the larger angle is □\square

Studdy Solution

STEP 1

1. Two angles are complementary if their measures add up to 90∘ 90^\circ .
2. Let the measure of the smaller angle be x x .
3. The measure of the larger angle is 9∘ 9^\circ more than twice the measure of the smaller angle.

STEP 2

1. Set up the equation based on the problem description.
2. Solve the equation to find the measure of the smaller angle.
3. Use the value of the smaller angle to find the measure of the larger angle.

STEP 3

Define the variables: Let x x be the measure of the smaller angle. The larger angle is then 2x+9∘ 2x + 9^\circ .

STEP 4

Set up the equation using the fact that the angles are complementary: x+(2x+9∘)=90∘ x + (2x + 9^\circ) = 90^\circ

STEP 5

Simplify the equation: x+2x+9∘=90∘ x + 2x + 9^\circ = 90^\circ 3x+9∘=90∘ 3x + 9^\circ = 90^\circ

STEP 6

Solve for x x : Subtract 9∘ 9^\circ from both sides: 3x=81∘ 3x = 81^\circ

STEP 7

Divide both sides by 3 to solve for x x : x=27∘ x = 27^\circ

STEP 8

Find the measure of the larger angle using the value of x x : 2x+9∘=2(27∘)+9∘ 2x + 9^\circ = 2(27^\circ) + 9^\circ =54∘+9∘ = 54^\circ + 9^\circ =63∘ = 63^\circ
The measure of the smaller angle is 27∘ \boxed{27^\circ} .
The measure of the larger angle is 63∘ \boxed{63^\circ} .

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