Chapter 4: Q. 355 (page 480)

The measure of one of the small angles of a right triangle is $15$ less than twice the measure of
the other small angle. Find the measure of both angles.

Short Answer

Expert verified

The measures of the angles are $55$ and $35$

Step by step solution

Step 1. Given information

The measure of one of the small angles of a right triangle is $15$ less than twice the measure of

the other small angle.

Step 2. Find the angles

Let angles to be $x$ and $y$

$x + y = 90$

Now using the given condition,

$x = 2 y - 15$

Put this value of $x$ in other equation,

$x + y = 90 2 y - 15 + y = 90 3 y = 105 y = 35$

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

$x + y = 90 x + 35 = 90 x = 55$

The measures of the angles are $35$ and $55$

Step 3. Check by substituting values in both the equations

Substitute $x = 55, y = 35$ in both the equations

$x + y = 90 55 + 35 = 90 90 = 90$

This is true

$x = 2 y - 15 55 = 2 (35) - 15 55 = 70 - 15 55 = 55$

This is also true

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The measure of one of the small angles of a right triangle is $15$ less than twice the measure of
the other small angle. Find the measure of both angles.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the angles

Step 3. Check by substituting values in both the equations

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The measure of one of the small angles of a right triangle is 15less than twice the measure ofthe other small angle. Find the measure of both angles.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the angles

Step 3. 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

Applied Mathematics

Pure Maths

Mechanics Maths

Probability and Statistics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

The measure of one of the small angles of a right triangle is $15$ less than twice the measure of
the other small angle. Find the measure of both angles.