Question

1. the diagram shows \\(\overleftrightarrow{mk}\\) intersecting \\(\overrightarrow{hj}\\) and \\(\overrightarrow{hl}\\) at point \\(h\\).

which angle relationship is relevant ?

Explanation:

Step1: Analyze the angle relationship

Since \( \overrightarrow{HJ}\) is perpendicular to \( \overrightarrow{HL}\), the sum of \((2x + 47)^{\circ}\), \((x - 32)^{\circ}\) and \(y^{\circ}\) is \(90^{\circ}\). But if we consider the straight - line \( \overrightarrow{ML}\) (assuming it's a straight line, as \( \overrightarrow{MK}\) intersects \( \overrightarrow{HL}\) and \( \overrightarrow{HJ}\) at \(H\)), the sum of \((2x + 47)^{\circ}\) and \((x - 32)^{\circ}\) is \(90^{\circ}\) (complementary angles, as \( \angle JHL = 90^{\circ}\)).

$$2x+47+x - 32=90$$

Step2: Solve the equation for \(x\)

Combine like terms:

$$3x+15 = 90$$

Subtract 15 from both sides:

$$3x=90 - 15$$

$$3x=75$$

Divide both sides by 3:

$$x = 25$$

Step3: Find \(y\)

Since \(y+(x - 32)=90\) (because \( \angle JHL=90^{\circ}\)), substitute \(x = 25\)

$$y+(25 - 32)=90$$

$$y-7 = 90$$

Add 7 to both sides:

$$y=97$$

The relevant angle relationship is that \((2x + 47)^{\circ}\) and \((x - 32)^{\circ}\) are complementary (their sum is \(90^{\circ}\)) because \( \overrightarrow{HJ}\perp\overrightarrow{HL}\) (right - angle formed at \(H\) between \( \overrightarrow{HJ}\) and \( \overrightarrow{HL}\)).

Answer:

The relevant angle relationship is that \((2x + 47)^{\circ}\) and \((x - 32)^{\circ}\) are complementary (sum to \(90^{\circ}\))