The measure of angle D is d.) 98°
To be able to answer the following problem, you need to understand some facts about an inscribed quadrilateral.
- An inscribed quadrilateral is a 4-sided polygon that has its 4 vertex angles at the circumference of a circle.
- Opposite angles of an inscribed quadrilateral are supplementary, which means they sum up to 180 degrees.
A diagram showing the inscribed quadrilateral ABCD is shown in the diagram attached below. The following assumptions can be made:
- ∠A and ∠C supplementary angles, ∴ m∠A + ∠C = 180
- ∠A and ∠C supplementary angles, ∴ ∠B = ∠D = 180
Create an equation to find the value of x:
Thus,
[tex]m<A = 64^{o} (given)\\m<C = (9x - 1)^{o} \\ 64^{o} + (9x - 1)^{o} = 180^{o} (supplementary-angles)\\Solve\\64 + 9x - 1 = 180\\63 + 9x = 180\\63 + 9x - 63 = 180 - 63\\9x = 117\\\frac{9x}{9} = \frac{117}{9}\\x = 13[/tex]
Find m∠D:
[tex]m<B = (6x + 4)^{o} (given)\\\\(6x + 4)^{o} + m<D = 180^{o} (supplementary - angles)\\[/tex]
Plug in the value of x
[tex](6(13) + 4) + m<D = 180\\82 + m<D = 180\\82 + m<D - 82 = 180 - 82 \\m<D = 98^{o}[/tex]
The measure of angle D is d.) 98°
Learn more about inscribed quadrilateral here:
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