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cluponka [151]
3 years ago
13

Given: Circle O with diameter LN and inscribed angle LMN Prove: is a right angle. What is the missing reason in step 5? Statemen

ts Reasons 1. circle O has diameter LN and inscribed angle LMN 1. given 2. is a semicircle 2. diameter divides into 2 semicircles 3. circle O measures 360o 3. measure of a circle is 360o 4. m = 180o 4. definition of semicircle 5. m∠LMN = 90o 5. ? 6. ∠LMN is a right angle 6. definition of right angle HL theorem inscribed angle theorem diagonals of a rhombus are perpendicular. formed by a tangent and a chord is half the measure of the intercepted arc.
Mathematics
1 answer:
ZanzabumX [31]3 years ago
3 0

Answer:

Inscribed angle theorem

Step-by-step explanation:

This theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the same arc on the circle.

In this case, the angle is ∠LMN and the arc is arc LN. Arc LN measures 180°,  because segment LN is the diameter of the circle. Then, by the theorem:

∠LMN = (1/2)*arc LN = (1/2)*180° = 90°

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