Question

$\angle 1$ and $\angle 2$ are supplementary angles. if $m\angle 1 = (x + 1)\degree$ and $m\angle 2 = (3x + 19)\degree$, then find the measure of $\angle 1$.

Explanation:

Step1: Recall supplementary angles property

Supplementary angles sum to \(180^\circ\), so \(m\angle1 + m\angle2 = 180^\circ\).
Substitute \(m\angle1=(x + 1)^\circ\) and \(m\angle2=(3x + 19)^\circ\) into the equation: \((x + 1)+(3x + 19)=180\).

Step2: Simplify and solve for \(x\)

Combine like terms: \(x + 3x+1 + 19 = 180\) → \(4x+20 = 180\).
Subtract 20 from both sides: \(4x=180 - 20=160\).
Divide by 4: \(x=\frac{160}{4}=40\).

Step3: Find \(m\angle1\)

Substitute \(x = 40\) into \(m\angle1=(x + 1)^\circ\): \(m\angle1=(40 + 1)^\circ = 41^\circ\).

Answer:

The measure of \(\angle1\) is \(41^\circ\).