A quadrilateral is shown with the following angles: Angle D = 98 degrees, Angle C = 90 degrees, Angle B = 69 degrees. Find the measure of Angle A.
Answer (2)
To find the measure of Angle A in a quadrilateral, we can use the fact that the sum of the interior angles of any quadrilateral is always 360 degrees.
Here's a step-by-step explanation to solve the problem:
Understand the Problem: We need to find the measure of Angle A given the measures of the other three angles. The quadrilateral has angles: ∠ D = 9 8 ∘ , ∠ C = 9 0 ∘ , and ∠ B = 6 9 ∘ .
Use the Interior Angle Sum Property of a Quadrilateral: The sum of all angles in a quadrilateral is always 360 degrees. Therefore: ∠ A + ∠ B + ∠ C + ∠ D = 36 0 ∘
Substitute the Known Values: Substitute the known values of angles into the equation: ∠ A + 6 9 ∘ + 9 0 ∘ + 9 8 ∘ = 36 0 ∘
Calculate the Sum of the Known Angles: 6 9 ∘ + 9 0 ∘ + 9 8 ∘ = 25 7 ∘
Solve for ∠ A : Subtract the sum of the known angles from 360 degrees to find ∠ A :
∠ A = 36 0 ∘ − 25 7 ∘ = 10 3 ∘
Therefore, the measure of Angle A is 10 3 ∘ . This solution uses basic properties of quadrilaterals to find the missing angle, which is a common task in middle school mathematics.
The measure of Angle A in the quadrilateral is 103 degrees. This is determined by using the principle that the sum of the interior angles in a quadrilateral is always 360 degrees. We calculated the sum of the other three angles and subtracted it from 360 degrees to find Angle A.
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