Work out the size of angle KMJ. Give your answer to the nearest degree.
Understand the Problem
The question is asking to calculate the size of angle KMJ in the given shape using the provided measurements and angles, rounding the answer to the nearest degree.
Answer
$141°$
Answer for screen readers
The size of angle KMJ is $141°$.
Steps to Solve
- Identify the Angles and Shape We have a quadrilateral (MLJK) and need to find angle KMJ. Using given angles:
- Angle KLM = 104°
- Angle KJL = 37°
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Calculate the Remaining Angle at K The sum of angles in a triangle is $180°$. We can find angle MKL using: $$ \text{Angle MKL} = 180° - \text{Angle KLM} - \text{Angle KJL} $$ Substituting the values: $$ \text{Angle MKL} = 180° - 104° - 37° $$ Calculate: $$ \text{Angle MKL} = 180° - 141° = 39° $$
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Find Angle KMJ Since angles PKM and PJM form a straight line, they add up to $180°$. Thus, $$ \text{Angle KMJ} = 180° - \text{Angle MKL} $$ Substituting the value: $$ \text{Angle KMJ} = 180° - 39° = 141° $$
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Round the Answer Since the problem requires rounding to the nearest degree, angle KMJ remains 141° as it is already a whole number.
The size of angle KMJ is $141°$.
More Information
The solution involves understanding angle properties and triangle angles. The relationship between the angles allows us to find the unknown angle by using the sum of angles in a triangle.
Tips
- Miscalculating the sum of angles, which can lead to an incorrect angle estimate.
- Forgetting that the angles around a point or on a straight line need to add up correctly (180° for straight line).
