Chapter 4: Q. 354 (page 480)

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

Short Answer

Expert verified

The measures of the angles are $73$ and $17$ .

Step by step solution

Step 1. Given information

Two angles are complementary.

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

Step 2. Forming linear equations

Let larger angle = $x$

Let smaller angle = $y$

Both the angles are complementary, So we get

$x + y = 90$

Using the condition given, we get

$x = 4 y + 5$

Step 3. Find value of angles

On substituting value of $x$ from one equation to another, we get

localid="1644525555584" $x + y = 90 4 y + 5 + y = 90 5 y + 5 = 90 5 y = 85 y = 17$

Now put value of $y$ in any of the equation,

$x + y = 90 x + 17 = 90 x = 73$

The measures of the angles are $73$ and $17$

Step 4. Check by substituting values in both the equations

Substitute $x = 73, y = 17$ in both the equations

$x + y = 90 73 + 17 = 90 90 = 90$

This is true

$x = 4 y + 5 73 = 4 (17) + 5 73 = 68 + 5 73 = 73$

This is also true

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Forming linear equations

Step 3. Find value of angles

Step 4. Check by substituting values in both the equations

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Two angles are complementary. The measure ofthe larger angle is five more than four times the measure of the smaller angle. Find the measuresof both angles.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Forming linear equations

Step 3. Find value of angles

Step 4. Check by substituting values in both the equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Applied Mathematics

Calculus

Study anywhere. Anytime. Across all devices.

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