𝘮∠𝘕𝘖𝘗=𝟤𝘹+𝟤,  𝘮∠𝘗𝘖𝘙=𝟥𝘹−𝟧,m normal angle upper P upper O upper R times equals 3 times sans-serif-italic x minus 5 comma and 𝘮∠𝘕𝘖𝘘=𝟣𝟣𝟦

Given the problem:

- \( m∠NOP = 2x + 2 \)
- \( m∠POR = 3x - 5 \)
- \( m∠NOQ = 114^\circ \)

It appears that angles \( ∠NOP \) and \( ∠POR \) are part of the same angle \( ∠NOQ \), which has a measure of \( 114^\circ \). This implies that:

\[
m∠NOP + m∠POR = m∠NOQ
\]

We can now set up the equation:

\[
(2x + 2) + (3x - 5) = 114
\]

Let's simplify and solve for \( x \):

\[
2x + 3x + 2 - 5 = 114
\]
\[
5x - 3 = 114
\]
\[
5x = 117
\]
\[
x = \frac{117}{5} = 23.4
\]

Now that we have \( x = 23.4 \), we can substitute it back into the expressions for \( m∠NOP \) and \( m∠POR \) to find the measures of these angles:

1. \( m∠NOP = 2x + 2 = 2(23.4) + 2 = 46.8 + 2 = 48.8^\circ \)
2. \( m∠POR = 3x - 5 = 3(23.4) - 5 = 70.2 - 5 = 65.2^\circ \)

Thus:
- \( m∠NOP = 48.8^\circ \)
- \( m∠POR = 65.2^\circ \)
- \( m∠NOQ = 114^\circ \) (which checks out since \( 48.8 + 65.2 = 114 \)).

Would you like more details or have any further questions?

Here are 5 related questions:
1. What are the types of angles formed by the sum of \( m∠NOP \) and \( m∠POR \)?
2. How can we verify if these angles form a linear pair?
3. Can we apply the exterior angle theorem here?
4. What would happen if \( m∠NOQ \) was a right angle?
5. How would the solution change if \( m∠POR \) was doubled?

**Tip**: Always check if the sum of angles equals a given total when angles are adjacent.

𝘮∠𝘕𝘖𝘗=𝟤𝘹+𝟤,  𝘮∠𝘗𝘖𝘙=𝟥𝘹−𝟧, and 𝘮∠𝘕𝘖𝘘=𝟣𝟣𝟦. Solve for x and find the measures of ∠NOP and ∠POR.

Solve for x in the angle addition problem where m∠NOP = 2x + 2, m∠POR = 3x - 5, and m∠NOQ = 114°. Learn how to apply the angle addition postulate and algebraic equations step-by-step. Suitable for Grades 7-10.

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