Question

if two angles form a linear pair and the (mangle1=(2x + 20)^{circ}) and (mangle2=(48x)^{circ}), find the measure of each angle. (mangle1 = 90^{circ}) and (mangle2 = 90^{circ}), (mangle1 = 26.4^{circ}) and (mangle2 = 153.6^{circ}), (mangle1 = 153.6^{circ}) and (mangle2 = 26.4^{circ}), (mangle1 = 24.6^{circ}) and (mangle2 = 110.4^{circ})

Explanation:

Step1: Recall linear - pair property

Linear - pair angles are supplementary, so \(m\angle1 + m\angle2=180^{\circ}\).
Given \(m\angle1=(2x + 20)^{\circ}\) and \(m\angle2=(48x)^{\circ}\), we set up the equation \((2x + 20)+48x=180\).

Step2: Combine like - terms

Combining the \(x\) terms, we get \(2x+48x + 20=180\), which simplifies to \(50x+20 = 180\).

Step3: Solve for \(x\)

Subtract 20 from both sides: \(50x=180 - 20=160\). Then divide both sides by 50: \(x=\frac{160}{50}=3.2\).

Step4: Find \(m\angle1\)

Substitute \(x = 3.2\) into the expression for \(m\angle1\): \(m\angle1=(2x + 20)^{\circ}=(2\times3.2+20)^{\circ}=(6.4 + 20)^{\circ}=26.4^{\circ}\).

Step5: Find \(m\angle2\)

Substitute \(x = 3.2\) into the expression for \(m\angle2\): \(m\angle2=(48x)^{\circ}=48\times3.2^{\circ}=153.6^{\circ}\).

Answer:

\(m\angle1 = 26.4^{\circ}\) and \(m\angle2 = 153.6^{\circ}\)