Questions: Segments and Angles Solving an equation involving complementary or supplementary angles In the figure below, m angle 1=(x-5)° and m angle 2=4x°. Find the angle measures.

Segments and Angles
Solving an equation involving complementary or supplementary angles

In the figure below, m angle 1=(x-5)° and m angle 2=4x°.
Find the angle measures.

Transcript text: Segments and Angles Solving an equation involving complementary or supplementary angles In the figure below, $m \angle 1=(x-5)^{\circ}$ and $m \angle 2=4 x^{\circ}$. Find the angle measures.

Solution

Solution Steps

Step 1: Identify the relationship between the angles

Since angles 1 and 2 form a straight line, they are supplementary. This means their measures add up to 180 degrees.

Step 2: Set up the equation

Given: \[ m \angle 1 = (x - 5)^\circ \] \[ m \angle 2 = 4x^\circ \] Since they are supplementary: \[ (x - 5) + 4x = 180 \]

Step 3: Solve for $ x $

Combine like terms: \[ 5x - 5 = 180 \] Add 5 to both sides: \[ 5x = 185 \] Divide by 5: \[ x = 37 \]

Step 4: Find the measures of the angles

Substitute $ x = 37 $ back into the expressions for the angles: \[ m \angle 1 = (37 - 5)^\circ = 32^\circ \] \[ m \angle 2 = 4 \times 37^\circ = 148^\circ \]