PQRS is a cyclic quadrilateral such that PR is a diameter of the circle. If ∠QPR = 670 and ∠SPR =720,then ∠QRS =
Question
PQRS is a cyclic quadrilateral such that PR is a diameter of the circle. If ∠QPR = 670 and ∠SPR =720,then ∠QRS =
Solution
Given that PQRS is a cyclic quadrilateral and PR is a diameter of the circle, we can use the properties of cyclic quadrilaterals to find the measure of angle QRS.
In a cyclic quadrilateral, opposite angles are supplementary. Therefore, we can find the measure of angle QRS by subtracting the given angles from 180 degrees.
∠QPR = 670 degrees ∠SPR = 720 degrees
To find ∠QRS, we subtract the given angles from 180 degrees:
∠QRS = 180 - ∠QPR - ∠SPR ∠QRS = 180 - 670 - 720 ∠QRS = 180 - 1390 ∠QRS = -1210
Since the measure of an angle cannot be negative, we can conclude that there is an error in the given information or the problem itself. Please double-check the values provided.
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