Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.
<h3>What is the Inscribed Angle Theorem?</h3>
Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).
m∠BAC = 40 degrees.
Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]
Corresponding arc BC = 80 degrees.
Arc AC through point B = 180 degrees [half circle]
Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.
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well, we know the "sum" of both angles is 90°, notice the rectangle in the corner, so we can say that the angles are simply complementary angles, thus
Answer: x = 18
explanation: the two angles are congruent bc so you can set the equation up as 9x - 40 = 5x + 32 and then solve for x
hope this helps :)