Answer:
A. 23+x=140
Step-by-step explanation:
The angle addition postulate states that the measure of a larger angle formed by two or more smaller angles placed side by side is the the sum of the smaller angles. The angle addition postulate states that if B is in the interior of AOC , then:
m∠AOB + m∠BOC = m∠AOC.
From the image:
∠NOP = ∠NOQ + ∠QOP
∠NOP = 140, ∠NOQ = x, ∠QOP = 23
substituting:
140 = x + 23
x = 140 - 23 = 117
∠NOQ = 117°
Since O is circumscribed about quadrilateral DEFG, the value of x is equal to: D. 68°.
<h3>What is a supplementary angle?</h3>A supplementary angle can be defined as two (2) angles or arc whose sum is always equal to 180 degrees. Mathematically, a supplementary angle can be calculated as follows:
Q + R = 180°.
In Geometry, the opposite angles of any cyclic quadrilateral that is inscribed inside a circle always form a supplementary angle. Thus, we would determine the value of x by using the mathematical expression above:
x + 112° = 180°
x = 180° - 112°
x = 68°
Read more on supplementary angle here: brainly.com/question/12542846
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