Question

Question ID: 77392514-9646-4d54-be90-9bb3240e80de

Points Possible: 1
Points Received: 0
Objective: Create multistep equations in one variable and use them to solve problems.
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In a triangle, the measure of the first angle is 24 degrees more than the measure of the second angle. The measure of the third angle is four times the
measure of the second angle. If the total number of degrees in a triangle is 180, what is the measure of the largest angle?
26 degrees
50 degrees
104 degrees
* 136 degrees

Answer 1

Let's denote the measure of the second angle as x. The measure of the largest angle is 4x, and solving the equation x + (x + 24) + 4x = 180 gives x = 26. Therefore, the largest angle measures 104 degrees.

Step-by-step explanation:

Let's denote the measure of the second angle as x. According to the given information, the measure of the first angle is x + 24 degrees, and the measure of the third angle is 4x degrees. Since the sum of the angles in a triangle is 180 degrees, we can set up the equation: x + (x + 24) + 4x = 180. Solving this equation, we find that 6x + 24 = 180. Subtracting 24 from both sides gives us 6x = 156. Dividing both sides by 6, we get x = 26. Therefore, the measure of the largest angle, which is the third angle, is 4x = 4(26) = 104 degrees, so the correct answer is 104 degrees.

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