Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A?

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Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A?

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Answer 1 · 2017-05-12T14:12:22

$m ∠ A = 77^{\circ}$ $mangleA=77^@$

Explanation:

Consider the property of cyclic quadrilaterals for which opposite angles are supplementary, then:
$m ∠ A + m ∠ C = 180^{\circ}$ $mangleA+mangleC=180^@$

Since we are given that $m ∠ A = {(2 x + 9)}^{\circ}$ $mangleA=(2x+9)^@$ and $m ∠ C = {(3 x + 1)}^{\circ}$ $mangleC=(3x+1)^@$ , we can substitute to find the value of $x$ $x$ :
$2 x + 9 + 3 x + 1 = 180$ $2x+9+3x+1=180$
$5 x + 10 = 180$ $5x+10=180$
$5 x = 170$ $5x=170$
$x = 34$ $x=34$

Now, we can substitute in the above value of $x$ $x$ to find $m ∠ A$ $mangleA$ :
$m ∠ A = {(2 x + 9)}^{\circ} = {(2 \cdot 34 + 9)}^{\circ} = 77^{\circ}$ $mangleA=(2x+9)^@=(2*34+9)^@=77^@$

Therefore, the $m ∠ A = 77^{\circ}$ $mangleA=77^@$

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Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A?

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Quadrilateral ABCD is inscribed in a circle. What is the measure of angle A?