2 angles are complementary. the measure of one angle is 15 degrees more than twice the other. What is the measure of the smaller angle?

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

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Here's how to set this up.  First you remember that complementary angles add up to 90 degrees, right?

So then you set up your equation using your other data.  We'll call one angle's measure "x" -- that will be the smaller one.  And we know that the other one is 15 degrees more than twice x.  How do you put that in mathematical terms?  Twice x is 2x, 15 more is +15.

So that gives us

90 = x + 2x + 15

So now we need to get all the x's on one side and the numbers on the other.  Subtract 15 from both sides.

x + 2x = 75 or 3x = 75.

Now you have to divide both sides by 3 so as to solve for x

x = 25

To check this, plug the numbers into the original equation.

15 more than twice 25 is 50+15 = 65.

So one of our angles is 25 degrees and the other is 65 (twice 25 + 15).  Those add up to 90 degrees so they're complementary.

jess1999's profile pic

jess1999 | Student, Grade 9 | (Level 1) Valedictorian

Posted on

First let " x " represent the smaller angle

First we should set up the equation. Since complementary angles add up to 90 degrees the equation should look like

90 = x + 2x + 15 now combine the like terms

By combining the like terms, your equation should be

90 = 3x + 15 now subtract 15 on both sides

By subtracting, your equation should be

75 = 3x now divide 3 on both sides

By dividing, your equation should be

25 = x

so the smallest angle = 25 degrees

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

2 angles are complementary. the measure of one angle is 15 degrees more than twice the other. What is the measure of the smaller angle?

Lets call the two angles x and y. 

x + y = 90 (Definition of complementary angles.)

x = 2y + 15

Given the two equations, its simple enough to solve for x. 

2y + 15 + y = 90

3y = 90 - 15 = 75

y = 75/3 = 25

x = 2(25) + 15 = 50 + 15 = 65

mettabear's profile pic

mettabear | Elementary School Teacher | eNotes Newbie

Posted on

Since complementary angles add up to 90 degrees you are looking to find the sum of two angles that add up to 90 degrees.

Let's call the small angle X. You said the bigger one is twice the small one plus 15. So twice X is 2a and 15 more is 2X+15.

So the equation is :

2X+15+X=90 

Because the small angle is X the bigger one 2X+15.

Adding the Xs together you get

3X+15=90

Subtracting 15 from both sides gives you

3X=75

Dividing both sides by 3 makes X become 25.

So your smaller angle is 25 degrees.

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