Use the figure at the right to answer questions 9-12.

9.) 5x - 18 = 4x + 7 10.) x = 25 11.) m∠MNQ = 107° 12.) m∠MNR = 73°

Step-by-step explanation:

9. & 10.)

∠MNQ and ∠RNP are vertical angles meaning they are equivalent to each other. Knowing that, we can set their values equal to each other and solve for x.

5x - 18 = 4x + 7 (Given)

x - 18 = 7 (Subtract 4x on both sides)

x = 25 (Add 18 on both sides)

Therefore, we know the equation is 5x - 18 = 4x + 7 and we know that x = 25.

Now we can solve for the angles.

11.)

5(25) - 18

125 - 18 = 107

Therefore, m∠MNQ = 107°.

12.)

∠MNR and ∠MNQ are supplementary angles meaning their angles will add up to 180°

∠MNR + 107 = 180

∠MNR = 73

Therefore, m∠MNR = 73°.

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