Question

In triangle ABC, if AC = CB, MZA = (3x + 18), mZB = (7x - 58), and mZC = (2x - 8), find the value of x and the measure of each angle. a) x = 8, mZA = 42°, mZB = 10°, mZC = 12° b) x = 10, mZA = 48°, mZB = 12°, mZC = 14° c) x = 6, mZA = 36°, mZB = 8°, mZC = 10° d) x = 12, mZA = 54°, mZB = 14°, mZC = 16°

Answer 1

To find the value of x and the measure of each angle, set up equations using the given information. Solve for x by equating congruent angles. Substitute the value of x to find each angle measure.

Step-by-step explanation:

To find the value of x and the measure of each angle in triangle ABC, we need to set up equations using the given information. Since AC = CB, angles ZA and ZC are congruent. Therefore, we can set up the equation 3x + 18 = 2x - 8 to find the value of x. Solving this equation, we find that x = 8.

To find the measure of each angle, we substitute the value of x into the given angle measures. We have ZA = 3(8) + 18 = 42°, ZB = 7(8) - 58 = 10°, and ZC = 2(8) - 8 = 12°. Therefore, the answer is a) x = 8, mZA = 42°, mZB = 10°, mZC = 12°.

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