AnswersGeometryInscribed Angles — QuizQuestion 31
31
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Inscribed Angles — Quiz

Question 31 • Geometry

Statements Reasons 1. circle cap o has diameter LN― and inscribed angle LMN 1. given 2. overarc LKN is a semicircle 2. diameter circle divides into 2 semicircles 3. circle cap o measures 360 degrees 3. measure of a circle is 360 degrees 4. m overarc LKN is equal to 180 degrees 4. definition of semicircle 5. m angle LMN is equal to 90 degrees 5. ? 6. angle LMN is a right angle 6. definition of right angle What is the missing reason in step 5?

Answer
A
diagonals of a rhombus are perpendicular.
B
inscribed angle theorem
C
angle formed by a tangent and a chord is half the measure of the intercepted arc.
D
HL theorem

Explanation

Step 4 establishes that the intercepted arc LKN measures 180°. By the inscribed angle theorem, an inscribed angle measures half the measure of its intercepted arc, so m∠LMN = 180° ÷ 2 = 90°. Therefore, the missing reason is the inscribed angle theorem.

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