Question

angle terminology with equations
question
∠1 and ∠2 are supplementary angles. if ( mangle1=(x - 25)^{circ} ) and ( mangle2=(x + 15)^{circ} ), then find the measure of ( angle1 ).
answer attempt 1 out of 3
submit answer

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(x - 25)^{\circ}\) and \(m\angle2=(x + 15)^{\circ}\) into the equation: \((x - 25)+(x + 15)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x-25+x + 15=(x+x)+(-25 + 15)=2x-10\).
The equation becomes \(2x-10 = 180\).

Step3: Solve for \(x\)

Add \(10\) to both sides: \(2x-10+10=180 + 10\), which gives \(2x=190\).
Divide both sides by \(2\): \(x=\frac{190}{2}=95\).

Step4: Find the measure of \(\angle1\)

Substitute \(x = 95\) into \(m\angle1=(x - 25)^{\circ}\).
\(m\angle1=(95 - 25)^{\circ}=70^{\circ}\).

Answer:

\(70\)