The sum of the measures of seven out of ten angles in a decagon is 1086^(@). If the three remaining angles are equal in measure, what is the measure of each angle?

Calculate Total Sum: First, we need to know the total sum of all angles in a decagon. A decagon has 10 sides, so we use the formula (n-2) * 180 to find the sum of its interior angles, where n is the number of sides. So, (10-2) * 180 = 8 * 180 = 1440 degrees is the total sum of all angles in a decagon.Find Sum of Remaining Angles: Next, we subtract the sum of the seven given angles from the total sum to find the sum of the remaining three angles. 1440 degrees - 1086 degrees = 354 degrees is the sum of the three equal angles.Calculate Measure of Each Angle: Finally, we divide the sum of the three equal angles by 3 to find the measure of each angle. 354 degrees ÷ 3 = 118 degrees. So, each of the three equal angles measures 118 degrees.

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The sum of the measures of seven out of ten angles in a decagon is
1086^(@). If the three remaining angles are equal in measure, what is the measure of each angle?

The sum of the measures of seven out of ten angles in a decagon is $1086^{\circ}$ . If the three remaining angles are equal in measure, what is the measure of each angle?

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Grade 7

Find missing angles in quadrilaterals II

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Q. The sum of the measures of seven out of ten angles in a decagon is

1086^{\circ}

. If the three remaining angles are equal in measure, what is the measure of each angle?

Calculate Total Sum: First, we need to know the total sum of all angles in a decagon. A decagon has $10$ sides, so we use the formula $(n-2) \times 180$ to find the sum of its interior angles, where $n$ is the number of sides. $\newline$ So, $(10-2) \times 180 = 8 \times 180 = 1440$ degrees is the total sum of all angles in a decagon.
Find Sum of Remaining Angles: Next, we subtract the sum of the seven given angles from the total sum to find the sum of the remaining three angles. $\newline$ $1440$ degrees $-$ $1086$ degrees $=$ $354$ degrees is the sum of the three equal angles.
Calculate Measure of Each Angle: Finally, we divide the sum of the three equal angles by $3$ to find the measure of each angle. $\newline$ $354$ degrees $\div 3 = 118$ degrees. So, each of the three equal angles measures $118$ degrees.