<DEF and <ABC are supplementary angles and <DEF is seven times as large as <ABC. Determine the measures of each angle. Students must show all work step by step to receive full credit.
supplementary angles= 180 degrees, therefore divide 180 by 7.
ABC = X deg.
DEF = 7X deg.
x + 7x = 180 deg.
8X = 180,
X = ABC = 22.5 deg.
7X = DEF = 7 * 22.5 = 157.5 deg.
To determine the measures of the angles, we need to set up an equation using the given information.
Let's assume the measure of angle <ABC is x degrees.
Since <DEF is seven times as large as <ABC, the measure of angle <DEF can be represented as 7x degrees.
We know that supplementary angles add up to 180 degrees. Therefore, we can set up the equation:
x + 7x = 180.
Combining like terms, we have:
8x = 180.
To isolate x, we can divide both sides of the equation by 8:
8x/8 = 180/8,
x = 22.5.
So, angle <ABC measures 22.5 degrees.
To find the measure of <DEF, we can substitute the value of x into the equation:
<DEF = 7(22.5) = 157.5.
Therefore, angle <DEF measures 157.5 degrees.
To summarize:
<ABC measures 22.5 degrees, and <DEF measures 157.5 degrees.