Question

question 2
sams wooden strips form four angles where they intersect. if one angle measures 60°, what is the measure of an adjacent angle (next to the 60° angle)?
60°
30°
question 3
sam labels two vertical angles in his frame as ( x ) and ( (2x - 30) )°.
solve for ( x ).
( x = )

Explanation:

Step1: Use the property of adjacent angles

Adjacent angles formed by intersecting lines are supplementary (sum to \(180^{\circ}\)). Let the adjacent angle be \(y\). We know \(60 + y=180\).

Step2: Solve for \(y\)

Subtract \(60\) from both sides: \(y = 180 - 60\).

Step3: Use the property of vertical angles

Vertical angles are equal. So \(x=(2x - 30)\).

Step4: Solve for \(x\) in the vertical - angles equation

Subtract \(x\) from both sides: \(0=2x - 30 - x\). Then \(x - 30=0\), so \(x = 30\).

Answer:

For the adjacent - angle problem: \(120^{\circ}\). For the vertical - angles problem: \(x = 30\).