Question

1. determine the value of unknown variables. give a reason for your answer

a) diagram: two intersecting lines with angles labeled ( 3x - 50 ) and ( 2x + 10 )
c) diagram: two intersecting lines with angles labeled ( 58^circ ) and ( 2x - 10 )

Explanation:

Part (a)

Step1: Identify vertical angles

Vertical angles are equal, so \(3x - 50 = 2x + 10\).

Step2: Solve for \(x\)

Subtract \(2x\) from both sides: \(3x - 2x - 50 = 2x - 2x + 10\)
\(x - 50 = 10\)
Add 50 to both sides: \(x - 50 + 50 = 10 + 50\)
\(x = 60\)

Part (c)

Step1: Identify supplementary angles (linear pair)

A linear pair of angles sums to \(180^\circ\), so \(58^\circ + (2x - 10)^\circ = 180^\circ\).

Step2: Solve for \(x\)

Simplify: \(2x + 48 = 180\)
Subtract 48: \(2x = 180 - 48\)
\(2x = 132\)
Divide by 2: \(x = \frac{132}{2}\)
\(x = 66\)

Answer:

• For part (a): \(x = 60\) (vertical angles are equal)
• For part (c): \(x = 66\) (linear pair angles sum to \(180^\circ\))