What is the size of angle α?
Understand the Problem
The question is asking to calculate the value of angle α in a quadrilateral, given the sizes of the other three angles (114°, 101°, and 82°). To solve it, we will use the fact that the sum of angles in a quadrilateral is 360°.
Answer
The size of angle $\alpha$ is $63^\circ$.
Answer for screen readers
The size of angle $\alpha$ is $63^\circ$.
Steps to Solve
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Understand the sum of angles in a quadrilateral The sum of all interior angles in a quadrilateral is always $360^\circ$.
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Add the known angles We will sum the three known angles: $$ 114^\circ + 101^\circ + 82^\circ $$
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Calculate the sum of the known angles Now perform the addition: $$ 114 + 101 + 82 = 297 $$
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Subtract from the total Subtract the sum of the known angles from $360^\circ$ to find angle $\alpha$: $$ \alpha = 360^\circ - 297^\circ $$
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Final calculation Perform the subtraction: $$ \alpha = 63^\circ $$
The size of angle $\alpha$ is $63^\circ$.
More Information
Each interior angle of a quadrilateral contributes to the total sum of $360^\circ$. Understanding this concept is crucial in solving problems related to polygons.
Tips
- Forgetting that the sum of angles in a quadrilateral is $360^\circ$.
- Incorrectly adding the known angles. To avoid this, carefully check your arithmetic.
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