Questions: Look at the quadrilateral below. Calculate the size of angle NPQ. Give your answer in degrees (°).

Look at the quadrilateral below. Calculate the size of angle NPQ. Give your answer in degrees (°).
Transcript text: Look at the quadrilateral below. Calculate the size of angle NPQ. Give your answer in degrees $\left(^{\circ}\right)$.
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Solution

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Solution Steps

Step 1: Identify the given angles
  • Angle \( \angle QRP = 35^\circ \)
  • Angle \( \angle PQN = 106^\circ \)
Step 2: Use the properties of a straight line
  • Since \( \angle PQN \) and \( \angle NPQ \) are on a straight line, their sum is \( 180^\circ \).
  • Therefore, \( \angle NPQ = 180^\circ - 106^\circ \).
Step 3: Calculate \( \angle NPQ \)
  • \( \angle NPQ = 180^\circ - 106^\circ = 74^\circ \).

Final Answer

  • The size of angle \( \angle NPQ \) is \( 74^\circ \).
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