Question

in the trapezium below, angle (b) is five times as large as angle (a).

work out the value of (a).

not drawn accurately

Explanation:

⚡ Using what you learned: lines and angles (parallel, transversal, vertical)

Step 1: Identify the relationship between angles

The top and bottom sides of the trapezium are parallel, as indicated by the arrows. The slanted side acts as a transversal line cutting across these parallel lines.

Angles \( a \) and \( b \) are interior angles on the same side of the transversal (co-interior angles). Co-interior angles between parallel lines always add up to \( 180^\circ \):

$$ a + b = 180^\circ $$

Step 2: Set up the equation

We are given that angle \( b \) is five times as large as angle \( a \):

$$ b = 5a $$

Substitute \( 5a \) for \( b \) in the angle sum equation:

$$ a + 5a = 180^\circ $$

Step 3: Solve for a

Combine like terms:

$$ 6a = 180^\circ $$

Divide both sides by \( 6 \):

$$ a = \frac{180^\circ}{6} $$

$$ a = 30^\circ $$

Answer:

\( 30^\circ \) (or \( 30 \))