Question

statement
x = 45-40
= 5
reason
vertically opposite

corrections

a + 63° = 180°
a = 180° - 63°
a = 117
suppl angle

x + 10° + 75° = 180
x = 180° - 85
x = 95°
sum ∠s on straight line

18 september, 2025
geometry of straight line
class activity / home activity

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

diagrams: a) two intersecting lines with angles (2x + 10) and (3x - 50); b) right - angle diagram with (63^circ) and (x); c) two intersecting lines with (58^circ) and (2x - 10^circ); table: statement (= 2x + 10 = 3x - 50), reason (=) vertically opposite; other rows with vertically opposite angles

Explanation:

Part a: Solving \(2x + 10 = 3x - 50\)

Step 1: Subtract \(2x\) from both sides

To isolate the variable \(x\), we subtract \(2x\) from each side of the equation. This gives us \(2x + 10 - 2x = 3x - 50 - 2x\), which simplifies to \(10 = x - 50\).

Step 2: Add 50 to both sides

Next, we add 50 to both sides to solve for \(x\). So, \(10 + 50 = x - 50 + 50\), which simplifies to \(60 = x\).

Step 1: Set the angles equal

Since the angles are vertically opposite, they are equal. So we set up the equation \(2x - 10 = 58\).

Step 2: Add 10 to both sides

Adding 10 to both sides gives \(2x - 10 + 10 = 58 + 10\), which simplifies to \(2x = 68\).

Step 3: Divide by 2

Dividing both sides by 2, we get \(\frac{2x}{2}=\frac{68}{2}\), so \(x = 34\).

Answer:

\(x = 60\) (Reason: Vertically opposite angles are equal, so we set the two expressions equal and solve for \(x\).)

Part c: Solving for \(x\) when angles are \(58^\circ\) and \(2x - 10^\circ\)