Questions: 422) Find the measure of each angle (10x+22x+17.808 #27) Two angles form a linear pair. The measure of one angle is three times the measure of the other angle. Find the measure of each angle.

422) Find the measure of each angle (10x+22x+17.808

#27) Two angles form a linear pair. The measure of one angle is three times the measure of the other angle. Find the measure of each angle.

Transcript text: 422) Find the measure of each angle (10x+22x+17.808 \#27) Two angles form a linear pair. The measure of one angle is three times the measure of the other angle. Find the measure of each angle.

Solution

Solution Steps

Step 1: Identify the relationship between the angles

The problem states that two angles form a linear pair. This means that the sum of the two angles is 180 degrees.

Step 2: Set up the equation

Let the measure of one angle be \( x \). Since the measure of the other angle is three times the measure of the first angle, it can be represented as \( 3x \).

Step 3: Formulate the equation

Since the angles form a linear pair, their sum is 180 degrees: \[ x + 3x = 180 \]

Step 4: Solve for \( x \)

Combine like terms: \[ 4x = 180 \] Divide both sides by 4: \[ x = 45 \]

Step 5: Find the measure of the other angle

Since the other angle is three times the measure of the first angle: \[ 3x = 3 \times 45 = 135 \]