Question

solving an equation involving complementary or supplementary angles
in the figure below, ( m angle 1=(x - 15)^{circ} ) and ( m angle 2 = 4x^{circ} ).
find the angle measures.
( m angle 1=square^{circ} )
( m angle 2=square^{circ} )

Explanation:

Step1: Use the supplementary angles property

Since \(\angle1\) and \(\angle2\) are supplementary, \(m\angle1 + m\angle2=180^{\circ}\). Substitute \(m\angle1=(x - 15)^{\circ}\) and \(m\angle2 = 4x^{\circ}\) into the equation: \((x-15)+4x=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+4x-15 = 180\), which gives \(5x-15=180\).

Step3: Solve for \(x\)

Add \(15\) to both sides: \(5x-15 + 15=180 + 15\), so \(5x=195\). Then divide both sides by \(5\): \(x=\frac{195}{5}=39\).

Step4: Find \(m\angle1\)

Substitute \(x = 39\) into \(m\angle1=(x - 15)^{\circ}\): \(m\angle1=(39-15)^{\circ}=24^{\circ}\).

Step5: Find \(m\angle2\)

Substitute \(x = 39\) into \(m\angle2 = 4x^{\circ}\): \(m\angle2=4\times39^{\circ}=156^{\circ}\).

Answer:

\(m\angle1 = 24^{\circ}\), \(m\angle2=156^{\circ}\)