Question

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

Answer 1

B. Inscribed Angle theorem

Explanation:

Answer 2

Inscribed angle theorem

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°