The measures of the angles of a triangle are in the extended ratio 3:5:7. What is the measure of the
smallest angle?
(1 point)
O 12°
36°
60°
O 84°
The angles of a triangle add up to 180 degrees.
Let's represent the extended ratio as 3x:5x:7x.
So, the sum of the angles is 3x + 5x + 7x = 15x.
We know that 15x = 180 (the sum of the angles of a triangle is 180 degrees), so x = 12.
Therefore, the angles are 36 degrees, 60 degrees, and 84 degrees.
The smallest angle is 36 degrees, so the answer is B) 36°.
To find the measure of the smallest angle in the triangle, we need to determine the value of the smallest ratio given in the extended ratio.
The given extended ratio is 3:5:7.
To find the smallest ratio, we need to add up the ratios and determine the value of the smallest ratio.
3 + 5 + 7 = 15
The smallest angle is represented by the ratio 3, so we need to determine what fraction of the total sum 3 represents.
The fraction for 3 is calculated as:
3 / 15 = 1/5
To find the measure of the smallest angle, we need to multiply the fraction by 180 degrees, which is the sum of the angle measures in a triangle.
1/5 * 180° = 36°
Therefore, the measure of the smallest angle in the triangle is 36°.