Math  /  Geometry

QuestionSpiral Review A triangle has angles measuring 45,5545^{\circ}, 55^{\circ}, and 8080^{\circ}. It is dilated by a scale factor of 2 . What are the angle measures, in order from least to greatest, of the dilated image? Enter the correct answers in the boxes.
Show Hints \square \square , and \square ]]^{\circ} \square

Studdy Solution

STEP 1

1. The sum of the angles in a triangle is always 180 180^\circ .
2. A dilation changes the size of a figure but not the angle measures.
3. The scale factor does not affect the angle measures of a triangle.

STEP 2

1. Verify the angle measures of the original triangle.
2. Determine the angle measures of the dilated triangle.
3. Order the angle measures from least to greatest.

STEP 3

Verify the angle measures of the original triangle by adding them together to ensure they sum to 180 180^\circ .
45+55+80=180 45^\circ + 55^\circ + 80^\circ = 180^\circ
The angle measures are correct for a triangle.

STEP 4

Understand that dilation does not change the angle measures. Therefore, the angles of the dilated triangle remain the same as the original triangle: 45,55, 45^\circ, 55^\circ, and 80 80^\circ .

STEP 5

Order the angle measures from least to greatest:
45,55,80 45^\circ, 55^\circ, 80^\circ
The angle measures of the dilated triangle, in order from least to greatest, are:
45,55,80 \boxed{45^\circ}, \boxed{55^\circ}, \boxed{80^\circ}

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