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Answer :
Sure! Let's solve the problem step-by-step:
We are asked to find the measures of two supplementary angles, where one angle measures 168° more than the other angle.
1. Let's use [tex]\( x \)[/tex] to represent the measure of one angle.
2. The measure of the other angle, which we'll call [tex]\( y \)[/tex], is given as 168° more than [tex]\( x \)[/tex]. So, we can write [tex]\( y = x + 168 \)[/tex].
Since these angles are supplementary, their measures add up to 180°. Thus, we have:
[tex]\[ x + y = 180 \][/tex]
Now we substitute [tex]\( y \)[/tex] from the second equation into the first equation:
[tex]\[ x + (x + 168) = 180 \][/tex]
Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 2x + 168 = 180 \][/tex]
Next, let's isolate [tex]\( 2x \)[/tex] by subtracting 168 from both sides:
[tex]\[ 2x = 180 - 168 \][/tex]
[tex]\[ 2x = 12 \][/tex]
Now, solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{12}{2} \][/tex]
[tex]\[ x = 6 \][/tex]
So, one angle measures 6°.
To find the measure of the supplementary angle [tex]\( y \)[/tex], we use the equation [tex]\( y = x + 168 \)[/tex]:
[tex]\[ y = 6 + 168 \][/tex]
[tex]\[ y = 174 \][/tex]
Therefore, the measures of the two supplementary angles are:
- One angle is 6°.
- The other angle is 174°.
We are asked to find the measures of two supplementary angles, where one angle measures 168° more than the other angle.
1. Let's use [tex]\( x \)[/tex] to represent the measure of one angle.
2. The measure of the other angle, which we'll call [tex]\( y \)[/tex], is given as 168° more than [tex]\( x \)[/tex]. So, we can write [tex]\( y = x + 168 \)[/tex].
Since these angles are supplementary, their measures add up to 180°. Thus, we have:
[tex]\[ x + y = 180 \][/tex]
Now we substitute [tex]\( y \)[/tex] from the second equation into the first equation:
[tex]\[ x + (x + 168) = 180 \][/tex]
Combine the [tex]\( x \)[/tex] terms:
[tex]\[ 2x + 168 = 180 \][/tex]
Next, let's isolate [tex]\( 2x \)[/tex] by subtracting 168 from both sides:
[tex]\[ 2x = 180 - 168 \][/tex]
[tex]\[ 2x = 12 \][/tex]
Now, solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{12}{2} \][/tex]
[tex]\[ x = 6 \][/tex]
So, one angle measures 6°.
To find the measure of the supplementary angle [tex]\( y \)[/tex], we use the equation [tex]\( y = x + 168 \)[/tex]:
[tex]\[ y = 6 + 168 \][/tex]
[tex]\[ y = 174 \][/tex]
Therefore, the measures of the two supplementary angles are:
- One angle is 6°.
- The other angle is 174°.
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