Answer:
m∠OPQ + (2x+16)° = 180°
Step-by-step explanation:
You need to know a couple of things about quadrilaterals.
- The sum of the internal angles is 360°
- Opposite angles of an inscribed quadrilateral total 180°.
An inscribed quadrilateral is one that has its vertices on a circle, as in the given figure.
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To actually solve the figure (find the measures of the angles), a two-step process is involved. First, you must find the value of x. You do that by making use of the fact that angles O and Q total 180°.
After you know the value of x, you can figure the measure of angle R, and make use of the fact that angles R and P total 180°.
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Here, you're not asked to solve the figure. Instead, you're asked how you might find angle P. You do that as described in the previous paragraph:
m∠OPQ + m∠ORQ = 180° . . . . . . . angles R and P total 180°
m∠OPQ + (2x+16)° = 180° . . . . . . . substitute (2x+16)° for m∠ORQ
This matches the first answer choice.
