We can conclude that the value of x is (∠MNP + 66)/8 and angle m∠RNM = ∠RNQ - ∠MNP + 78.
<h3>What are angles?</h3>
An angle is a figure in Euclidean geometry formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle.
Angles formed by two rays are located in the plane containing the rays.
Angles are also formed when two planes intersect.
These are known as dihedral angles.
So,
∠MNQ = ∠MNP + ∠PNQ
8x + 12 = ∠MNP + 78
8x + 12 - 78 = ∠MNP
8x - 66 = ∠MNP
8x = ∠MNP + 66
x = (∠MNP + 66)/8
Now, substitute 'x = (∠MNP + 66)/8' in 8x + 12:
∠MNQ = 8x + 12
∠MNQ = 8 ×(∠MNP + 66)/8 + 12
∠MNQ = ∠MNP + 66 + 12
∠MNQ = ∠MNP + 78
Hence, m∠RNM = ∠RNQ - ∠MNP + 78
Therefore, in the given question value of x is (∠MNP + 66)/8 and angle m∠RNM = ∠RNQ - ∠MNP + 78.
