Question

∠1 and ∠2 are supplementary angles. if ( mangle1 = (x - 23)^circ ) and ( mangle2 = (x - 7)^circ ), then find the measure of ( angle1 ).

Explanation:

Step1: Recall supplementary angles property

Supplementary angles add up to \(180^\circ\). So, \(m\angle1 + m\angle2 = 180^\circ\).

Step2: Substitute the given expressions

Substitute \(m\angle1=(x - 23)^\circ\) and \(m\angle2=(x - 7)^\circ\) into the equation: \((x - 23)+(x - 7)=180\).

Step3: Simplify the left - hand side

Combine like terms: \(x+x-23 - 7=180\), which simplifies to \(2x-30 = 180\).

Step4: Solve for x

Add 30 to both sides: \(2x=180 + 30=210\). Then divide both sides by 2: \(x=\frac{210}{2}=105\).

Step5: Find the measure of \(\angle1\)

Substitute \(x = 105\) into the expression for \(m\angle1\): \(m\angle1=(105 - 23)^\circ=82^\circ\).

Answer:

The measure of \(\angle1\) is \(82^\circ\)