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The measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°
Explanation:
Given that the quadrilateral ABCD is inscribed in a circle.
The given angles are ∠A = (2x + 3), ∠C = (2x + 1) and ∠D = (x - 10)
We need to determine the measures of the angles A, C and D
<u>The value of x:</u>
We know that, the opposite angles of a cyclic quadrilateral add up to 180°
Thus, we have,
Substituting the values, we have,
Thus, the value of x is 44.
<u>Measure of ∠A:</u>
Substituting in ∠A = (2x + 3)°, we get,
Thus, the measure of angle A is 91°.
<u>Measure of ∠C :</u>
Substituting in ∠C = (2x + 1)°, we get,
Thus, the measure of angle C is 89°.
<u>Measure of ∠D :</u>
Substituting in ∠D = (x - 10)°, we get,
Thus, the measure of angle D is 34°.
Hence, the measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°