Question

Find m2CMN if m/LMC = 71x + 1,
m/LMN = 118°, and m/CMN = 45x + 1.
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Answer 1

To find the measure of angle CMN (m∠CMN), you can use the angle sum property for triangles. In a triangle, the sum of the angles is always 180 degrees.

You have the following angle measures:

m∠LMC = 71x + 1

m∠LMN = 118°

m∠CMN = 45x + 1

According to the angle sum property for triangle LMN:

m∠LMC + m∠LMN + m∠CMN = 180°

Now, plug in the given angle measures:

(71x + 1) + 118° + (45x + 1) = 180°

Combine like terms:

71x + 45x + 1 + 118 + 1 = 180

Combine constants:

116x + 120 = 180

Now, subtract 120 from both sides:

116x = 180 - 120

116x = 60

Now, divide by 116:

x = 60 / 116

x = 15 / 29

Now that you've found the value of x, you can find the measure of angle CMN (m∠CMN) by plugging it into the expression:

m∠CMN = 45x + 1

m∠CMN = 45(15/29) + 1

To simplify:

m∠CMN = (675/29) + 1

Now, find a common denominator:

m∠CMN = (675/29) + (29/29)

Combine fractions:

m∠CMN = (675 + 29) / 29

m∠CMN = 704 / 29

So, the measure of angle CMN (m∠CMN) is 704/29 degrees.

Answer 2

To find \(m\angle CMN\), we'll use the Angle Addition Postulate, which states that the measure of an angle formed by two adjacent angles is the sum of the measures of those two angles.

Given:

1. \(m\angle LMC = 71x + 1\)

2. \(m\angle LMN = 118°\)

3. \(m\angle CMN = 45x + 1\)

Since \(\angle LMC\), \(\angle LMN\), and \(\angle CMN\) are adjacent angles, we can set up the following equation:

\[m\angle LMC + m\angle CMN = m\angle LMN\]

Substitute the given values:

\[(71x + 1) + (45x + 1) = 118\]

Now, solve for \(x\):

\[116x + 2 = 118\]

\[116x = 116\]

\[x = 1\]

Now that we have the value of \(x\), we can find \(m\angle CMN\):

\[m\angle CMN = 45x + 1 = 45(1) + 1 = 46\]

So, \(m\angle CMN = 46°\).

Explanation:

I hope this helps you.