<D is complentary to <E and <D is supplementary to <G
If the measure of <E is 78
find the measure of <D and <G
To find the measure of angle <D and angle <G, we can use the relationship given.
If <D is complementary to <E, it means that the sum of <D and <E is 90 degrees, since complementary angles add up to 90 degrees.
So, <D + <E = 90 degrees.
Given that the measure of <E is 78 degrees, we can substitute this value into the equation:
<D + 78 = 90 degrees.
To find the measure of angle <D, we can isolate <D by subtracting 78 from both sides of the equation:
<D = 90 degrees - 78 degrees.
<D = 12 degrees.
Therefore, the measure of angle <D is 12 degrees.
Now, if <D is supplementary to <G, it means that the sum of <D and <G is 180 degrees because supplementary angles add up to 180 degrees.
So, <D + <G = 180 degrees.
We have already determined that the measure of angle <D is 12 degrees, so substituting this value into the equation:
12 + <G = 180 degrees.
To find the measure of angle <G, we can isolate <G by subtracting 12 from both sides of the equation:
<G = 180 degrees - 12 degrees.
<G = 168 degrees.
Therefore, the measure of angle <G is 168 degrees.
To find the measure of <D and <G, we can use the properties of complementary and supplementary angles.
We are given that <D is complementary to <E, which means the sum of <D and <E is equal to 90 degrees (because complementary angles add up to 90 degrees).
We know that <E is 78 degrees, so we can substitute this value into the equation: <D + 78 = 90.
Subtracting 78 from both sides of the equation, we get: <D = 90 - 78 = 12 degrees.
Now, we are also given that <D is supplementary to <G, meaning the sum of <D and <G is equal to 180 degrees (because supplementary angles add up to 180 degrees).
Since we found that <D = 12 degrees, we can substitute this value into the equation: 12 + <G = 180.
Subtracting 12 from both sides of the equation, we get: <G = 180 - 12 = 168 degrees.
Therefore, the measure of <D is 12 degrees and the measure of <G is 168 degrees.