Use the image to answer the question.
A triangle a b c is shown with angle a measuring 4 x plus 14, angle b measuring 5 x plus 4, and angle c measuring 6 x minus 3.
Use the Triangle Angle Sum Theorem to find the measure of the angles for the triangle in the diagram.
(1 point)
Responses
54°, 44°, and 82°
54 degrees , 44 degrees , and 82 degrees
59°, 58°, and 63°
59 degrees , 58 degrees , and 63 degrees
57°, 54°, and 69°
57 degrees , 54 degrees , and 69 degrees
59°, 63°, and 48°
59 degrees , 63 degrees , and 48 degrees
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The Triangle Angle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees.
Given that angle A measures 4x + 14, angle B measures 5x + 4, and angle C measures 6x - 3, we can set up the equation:
(4x + 14) + (5x + 4) + (6x - 3) = 180
Combining like terms, we get:
15x + 15 = 180
Subtracting 15 from both sides, we have:
15x = 165
Dividing both sides by 15, we get:
x = 11
Now we can substitute x = 11 back into the expressions for each angle:
Angle A = 4(11) + 14 = 58 degrees
Angle B = 5(11) + 4 = 59 degrees
Angle C = 6(11) - 3 = 63 degrees
So, the measure of the angles for the triangle in the diagram are 58 degrees, 59 degrees, and 63 degrees.
The correct answer is: 58°, 59°, and 63°
you shure
Yes, I am sure. Based on the given information and using the Triangle Angle Sum Theorem, the measure of the angles for the triangle in the diagram is 58 degrees, 59 degrees, and 63 degrees.
you one of the answers
Apologies for the confusion in my previous response. Let's solve the equation again:
(4x + 14) + (5x + 4) + (6x - 3) = 180
Combining like terms:
15x + 15 = 180
Subtracting 15 from both sides:
15x = 165
Dividing both sides by 15:
x = 11
Now replacing x with 11 in the expressions for each angle:
Angle A = 4(11) + 14 = 58 degrees
Angle B = 5(11) + 4 = 59 degrees
Angle C = 6(11) - 3 = 63 degrees
Therefore, the correct answer is: 58°, 59°, and 63°.
that is not one of the answers
I apologize for the confusion. In that case, we need to further evaluate the given options. Let's go through each option and determine if it matches the calculated angle measures:
1. 54°, 44°, and 82°:
This set of angles does not match the calculated angle measures of 58°, 59°, and 63°. So this option is not correct.
2. 59°, 58°, and 63°:
This set of angles matches the calculated angle measures of 58°, 59°, and 63°. So this option is correct.
3. 57°, 54°, and 69°:
This set of angles does not match the calculated angle measures of 58°, 59°, and 63°. So this option is not correct.
4. 59°, 63°, and 48°:
This set of angles does not match the calculated angle measures of 58°, 59°, and 63°. So this option is not correct.
Based on the evaluation, the correct answer is:
59°, 58°, and 63°