Sure, let's break this down step by step.
First, let's recall that supplementary angles are two angles whose measures add up to 180 degrees. Let's denote the measure of one angle as [tex]\( x \)[/tex] degrees.
Given in the problem, one angle measures 6 degrees less than twice the other angle. Let's establish our equations based on this information.
If one angle is [tex]\( x \)[/tex], then the other angle would be:
[tex]\[ 180 - x \][/tex] degrees (since the angles are supplementary and their sum must be 180 degrees).
According to the problem, one angle measures 6 degrees less than twice the other angle. This can be translated into the following equation:
[tex]\[ x = 2(180 - x) - 6 \][/tex]
Next, we'll solve for [tex]\( x \)[/tex]:
1. Distribute and simplify the equation:
[tex]\[ x = 360 - 2x - 6 \][/tex]
2. Combine like terms:
[tex]\[ x + 2x = 360 - 6 \][/tex]
[tex]\[ 3x = 354 \][/tex]
3. Solve for [tex]\( x \)[/tex] by dividing both sides of the equation by 3:
[tex]\[ x = \frac{354}{3} \][/tex]
[tex]\[ x = 118 \][/tex]
Thus, one of the angles measures 118 degrees.
Now, to find the measure of the other angle, we subtract this value from 180 degrees:
[tex]\[ 180 - 118 = 62 \][/tex]
So, the measures of the two supplementary angles are:
[tex]\[ 118 \text{ degrees} \][/tex] and [tex]\[ 62 \text{ degrees} \][/tex]
Therefore, the two supplementary angles are 118 degrees and 62 degrees.
