Math / Geometry

QuestionSave \& Exit Certify Lesson: 7.4 11.1b Systems of Equations Ap... WILLIAM BURRIS
Question 2 of 10, Step 1 of 1 0/10 Correct 1
Two angles are complementary if the sum of their measures is $90^{\circ}$ . Find two complementary angles such that the smaller angle is $57^{\circ}$ less than 2 times the larger angle. (Round to two decimal places if necessary.)
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Studdy Solution

STEP 1

1. Two angles are complementary if their sum is $90^\circ$ .
2. Let $x$ be the measure of the larger angle.
3. The smaller angle is $57^\circ$ less than twice the larger angle.

STEP 2

1. Set up the equation based on the problem description.
2. Solve the equation for the larger angle.
3. Calculate the smaller angle using the larger angle.

STEP 3

Define the variables: - Let $x$ be the larger angle. - The smaller angle is $2x - 57^\circ$ .

STEP 4

Set up the equation for complementary angles: $x + (2x - 57^\circ) = 90^\circ$

STEP 5

Simplify and solve the equation: $x + 2x - 57^\circ = 90^\circ$ $3x - 57^\circ = 90^\circ$

STEP 6

Add $57^\circ$ to both sides to isolate the terms with $x$ : $3x = 90^\circ + 57^\circ$ $3x = 147^\circ$

STEP 7

Divide both sides by 3 to solve for $x$ : $x = \frac{147^\circ}{3}$ $x = 49^\circ$

STEP 8

Calculate the smaller angle using the larger angle: $\text{Smaller angle} = 2x - 57^\circ$ $= 2(49^\circ) - 57^\circ$ $= 98^\circ - 57^\circ$ $= 41^\circ$
The two complementary angles are: - Larger angle: $\boxed{49^\circ}$ - Smaller angle: $\boxed{41^\circ}$

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Studdy Solution

STEP 1

1. Two angles are complementary if their sum is $90^\circ$ .
2. Let $x$ be the measure of the larger angle.
3. The smaller angle is $57^\circ$ less than twice the larger angle.

STEP 2

1. Set up the equation based on the problem description.
2. Solve the equation for the larger angle.
3. Calculate the smaller angle using the larger angle.

STEP 3

Define the variables: - Let $x$ be the larger angle. - The smaller angle is $2x - 57^\circ$ .

STEP 4

Set up the equation for complementary angles: $x + (2x - 57^\circ) = 90^\circ$

STEP 5

Simplify and solve the equation: $x + 2x - 57^\circ = 90^\circ$ $3x - 57^\circ = 90^\circ$

STEP 6

Add $57^\circ$ to both sides to isolate the terms with $x$ : $3x = 90^\circ + 57^\circ$ $3x = 147^\circ$

STEP 7

Divide both sides by 3 to solve for $x$ : $x = \frac{147^\circ}{3}$ $x = 49^\circ$

STEP 8

Calculate the smaller angle using the larger angle: $\text{Smaller angle} = 2x - 57^\circ$ $= 2(49^\circ) - 57^\circ$ $= 98^\circ - 57^\circ$ $= 41^\circ$
The two complementary angles are: - Larger angle: $\boxed{49^\circ}$ - Smaller angle: $\boxed{41^\circ}$

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Studdy Solution

STEP 1

1. Two angles are complementary if their sum is 90∘ 90^\circ 90∘.2. Let x x x be the measure of the larger angle.3. The smaller angle is 57∘ 57^\circ 57∘ less than twice the larger angle.

STEP 2

1. Set up the equation based on the problem description.2. Solve the equation for the larger angle.3. Calculate the smaller angle using the larger angle.

STEP 3

Define the variables: - Let x x x be the larger angle. - The smaller angle is 2x−57∘ 2x - 57^\circ 2x−57∘.

STEP 4

Set up the equation for complementary angles: x+(2x−57∘)=90∘ x + (2x - 57^\circ) = 90^\circ x+(2x−57∘)=90∘

STEP 5

Simplify and solve the equation: x+2x−57∘=90∘ x + 2x - 57^\circ = 90^\circ x+2x−57∘=90∘ 3x−57∘=90∘ 3x - 57^\circ = 90^\circ 3x−57∘=90∘

STEP 6

Add 57∘ 57^\circ 57∘ to both sides to isolate the terms with x x x: 3x=90∘+57∘ 3x = 90^\circ + 57^\circ 3x=90∘+57∘ 3x=147∘ 3x = 147^\circ 3x=147∘

STEP 7

Divide both sides by 3 to solve for x x x: x=147∘3 x = \frac{147^\circ}{3} x=3147∘​ x=49∘ x = 49^\circ x=49∘

STEP 8

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1. Two angles are complementary if their sum is $90^\circ$ .
2. Let $x$ be the measure of the larger angle.
3. The smaller angle is $57^\circ$ less than twice the larger angle.

1. Set up the equation based on the problem description.
2. Solve the equation for the larger angle.
3. Calculate the smaller angle using the larger angle.

Define the variables: - Let $x$ be the larger angle. - The smaller angle is $2x - 57^\circ$ .

Set up the equation for complementary angles: $x + (2x - 57^\circ) = 90^\circ$

Simplify and solve the equation: $x + 2x - 57^\circ = 90^\circ$ $3x - 57^\circ = 90^\circ$

Add $57^\circ$ to both sides to isolate the terms with $x$ : $3x = 90^\circ + 57^\circ$ $3x = 147^\circ$

Divide both sides by 3 to solve for $x$ : $x = \frac{147^\circ}{3}$ $x = 49^\circ$