Chapter 4: Q 4.34 (page 394)

Translate to a system of equations and then solve:
The difference of two complementary angles is $80$ degrees. Find the measures of the angles.

Short Answer

Expert verified

The measure of angles are $85^{\circ}$ and $5^{\circ}$ .

Step by step solution

Step 1. Given

We are given that the difference between two complementary angles is $80^{\circ}$ .

Step 2. Formation of equations

We know that the sum of complementary angles is equal to $90^{\circ}$ .

Let the one angle be $x$ , and the other angle will be $y$ , so the equation will be,

localid="1644600128864" $x + y = 90^{\circ} y = 90^{\circ} - x$ ,

The difference between the angles is $80^{\circ}$ , so the equation will be,

$x - y = 80^{\circ} x - (90^{\circ} - x) = 80^{\circ}$

Step 3. Solving the equation.

Solving $x - (90^{\circ} - x) = 80^{\circ}$

$x - 90^{\circ} + x = 80^{\circ} 2 x - 90^{\circ} = 80^{\circ} 2 x = 80^{\circ} + 90^{\circ} 2 x = 170^{\circ}$

Dividing by $2$ , we get

$x = 85^{\circ}$

And the other angle will be $90^{\circ} - 85^{\circ} = 5^{\circ}$ .

Step 4. Checking the solution

Checking the solution by putting the value of $x, y$ in the equations, we get

$x + y = 90^{\circ} 85^{\circ} + 5^{\circ} = 90^{\circ} 90^{\circ} = 90^{\circ} x - y = 80^{\circ} 85^{\circ} - 5^{\circ} = 80^{\circ} 80^{\circ} = 80^{\circ}$

This is true, hence the solution is correct.

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Translate to a system of equations and then solve:
The difference of two complementary angles is $80$ degrees. Find the measures of the angles.

Short Answer

Step by step solution

Step 1. Given

Step 2. Formation of equations

Step 3. Solving the equation.

Step 4. Checking the solution

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Translate to a system of equations and then solve:The difference of two complementary angles is 80degrees. Find the measures of the angles.

Short Answer

Step by step solution

Step 1. Given

Step 2. Formation of equations

Step 3. Solving the equation.

Step 4. Checking the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Statistics

Decision Maths

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Translate to a system of equations and then solve:
The difference of two complementary angles is $80$ degrees. Find the measures of the angles.