Calculate the sum of interior angles

For a polygon with $n$ sides, the sum of interior angles is $(n-2) \times 180°$. For a pentagon ($n=5$), the sum is $(5-2) \times 180° = 3 \times 180° = 540°$.

$(5-2) \times 180° = 540°$

Set up the ratio equation

Let the angles be $x, 2x, 3x, 4x, 5x$. Their sum must equal $540°$.

$x + 2x + 3x + 4x + 5x = 540°$

Solve for the multiplier x

Combining terms, we get $15x = 540°$. Dividing both sides by 15 gives $x = 36°$.

$15x = 540° \implies x = 36°$

Find the largest angle

The largest angle is $5x$. Substituting $x = 36°$, we get $5 \times 36° = 180°$. (Note: Given the official key claims 150, please check if the polygon was meant to be a different shape or ratio).

$5x = 5 \times 36° = 180°$