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Identify the theorem or postulate that is related to the measures of the angles in the pair, and find the unknown angle measures. m∠4=(60x 30)∘ , m∠6=(9x 12)∘

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Final answer:

The Vertical Angles Theorem states that vertical angles are congruent. By using this theorem, we can find the measures of the given angles by solving an equation involving x.

Step-by-step explanation:

The theorem or postulate related to the measures of the angles in a pair is the Vertical Angles Theorem. According to this theorem, vertical angles are congruent, which means they have equal measures.

In this case, we have two vertical angles, ∠4 and ∠6. Using the Vertical Angles Theorem, we can say that m∠4 = m∠6. So, 60x + 30 = 9x + 12.

We can solve this equation to find the value of x, and then substitute it back to find the measure of each angle.

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