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°

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:

Reply 6

The reply is B) Inscribed Angle Theorem

Reply 7

As a result of OL = OM = ON = the radius, subsequently every of ΔOLM and ΔONM is an isosceles triangle.ΔOLM has two equal angles denoted by a, and ΔONM has two equal angles denoted by b. The central angles x and y add as much as 180° on a straight line, sox + y = 180 (1) As a result of angles in a triangle sum to 180°, thereforex + 2a = 180 (2)y + 2b = 180 (3) Add (2) and (3) to obtainx + y + 2(a + b) = 360 From (1), obtain180 + 2(a + b) = 3602(a + b) = 180a + b = 90 As a result of (a + b) = ∠LMN, it proves that ∠LMN = 90°

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