French is the language spoken by the most inhabitants.
Explanation:
The map that is given in the question is of the country Canada. The language which is spoken most in Canada is French which is spoken by the most inhabitants there.
This is the language which allows the people to share and communicate their ideas and thoughts with one another in the country which has people living in it who are coming from different parts of the world.
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.
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Answer:
inscribed angle theorem
Explanation:
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Final answer:
The missing reason in step 5 is the Inscribed Angle Theorem, which states that the measure of an inscribed angle is half the measure of its intercepted arc. In this case, the intercepted arc is a semicircle, hence angle LMN is a right angle measuring 90 degrees.
Explanation:
To prove that angle LMN in a circle with diameter LN is a right angle, we rely on the Inscribed Angle Theorem, which states that the measure of an inscribed angle is half the measure of its intercepted arc. In this case, the intercepted arc is a semicircle, which measures 180 degrees. Therefore, the measure of angle LMN is half of 180 degrees.
Thus, the measure of angle LMN is 90 degrees. Going through the steps provided:
Circle O has diameter LN and inscribed angle LMN.LN is a semicircle.Circle O measures 360 degrees.m∡LN (arc) = 180 degrees.m∠LMN = 90 degrees (missing reason is Inscribed Angle Theorem).∠LMN is a right angle (definition of right angle).