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

Given: Circle O with diameter LN and inscribed angle LMN Show: is a proper angle. What’s the lacking purpose in step 5? Statements Causes 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 proper angle 6. definition of proper angle HL theorem inscribed angle theorem diagonals of a rhombus are perpendicular. fashioned by a tangent and a chord is half the measure of the intercepted arc. Mark this and return Save and Exit

B inscribed angel theorem Rationalization:

inscribed angle theorem Rationalization: simply took quiz on edgen

Inscribed angle theorem Step-by-step clarification: This theorem states that an angle θ inscribed in a circle is half of the central angle 2θ that subtends the identical arc on the circle. On this case, the angle is ∠LMN and the arc is arc LN. Arc LN measures 180°,  as a result of phase LN is the diameter of the circle. Then, by the theory: ∠LMN = (1/2)*arc LN = (1/2)*180° = 90°

Also Read :   Which process forms ridges and valleys?

Technique 1. Take a look at the image 1. We’ve: Image 2. —————————————————————————————— Technique 2. (Image 3) ΔLOM and ΔMON are isosceles triangles. Due to this fact the 2 angles reverse the legs are equal. The sum of the interior angles in every triangle is 180°. Thereofre in ΔLMN we now have:

step 5=  inscribed angle theorem Rationalization: