Question

1. what is the measure of the third angle of a triangle whose other two angle measures are 79° and 43°? 101° a 72° b 58° c 43° d 19. find the value of y. 2.5 a 4 b 10 c 5 d 20. find the value of x. 10 a 2 b 5 c 25 d

Explanation:

18.

Step1: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). Let the third - angle be \(x\). Then \(x + 79^{\circ}+43^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

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Step1: Set up the equation based on the segment - addition postulate

Since \(AB=AC + CB\), we have \(5y-5=3y + 15\).

Step2: Solve the linear equation for \(y\)

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Step1: Assume the two angles are supplementary (if they are same - side interior angles)

If the two lines are parallel and cut by a transversal, then \((4x - 15)+(15x+5)=180\) (same - side interior angles are supplementary).

Step2: Simplify the left - hand side of the equation

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Step3: Solve for \(x\)

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Answer:

C. \(58^{\circ}\)

19.