The sum of the measures of angles of a quadrilateral and that of a triangle is

A) $180^{\circ}$

B) $360^{\circ}$

C) $540^{\circ}$

D) $720^{\circ}$

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The correct answer is C) $540^{\circ}$.

To solve this, consider the properties of geometric shapes:

  • The sum of the interior angles of a quadrilateral totals $360^{\circ}$.
  • The sum of the interior angles of a triangle is $180^{\circ}$.

To find the total sum of the angles for both a quadrilateral and a triangle, we simply add these sums:

$$ 360^{\circ} + 180^{\circ} = 540^{\circ} $$

Thus, the combined sum of the angles is $540^{\circ}$.

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