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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 4: Q 99. (page 405)

Two angles are complementary. The measure of the larger angle is ten more than four times the measure of the smaller angle. Find the measures of both angles.

Short Answer

Expert verified

The measures of angles are $74$ and $16$

Step by step solution

01

Step 1. Given information

Step 1. Given information

Suppose $x$ represents the measure of the first angle.

and similarly, $y$ represents the measure of the second angle

Now, both the angles are complementary

Therefore,

$x + y = 90$

02

Step 2. Creating the equation

The measures of the larger angle is ten more than four times the measure of the smaller angle.

Therefore, $x = 10 + 4 y$

03

Step 3. Finding the value y

Substitute the value of $x = 10 + 4 y$ in the equation

Therefore,

$10 + 4 y + y = 90$

$10 + 5 y = 90$

$5 y = 80$

$y = \frac{80}{5}$

$= 16$

04

Step 4. Finding the value x

Put, $y = 16$ into $x = 10 + 4 y$ and solve for x

$x = 10 + 4 y x = 10 + 4 (16)$

$= 10 + 64$

$= 74$

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Most popular questions from this chapter

Write an application problem similar to Example $4.14$ . Then translate to a system of equations and solve it.

In a system of linear equations, the two equations have the same intercepts. Describe the possible solutions to the system.

Solve the system by graphing: $\{\begin{cases} x - 3 y = - 3 \\ x + y = 5 \end{cases}$

Solve the system by graphing: $\{\begin{cases} - x + y = 1 \\ 2 x + y = 10 \end{cases}$ $\{\begin{cases} - x + y = 1 \\ 2 x + y = 10 \end{cases}$

Solve the system by substitution:

\{\begin{cases} 4 x - y = 0 \\ 2 x - 3 y = 5 \end{cases}

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