<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

D+E=90 ... (1)

D+G=180 ... (2)

Given E=78,
Solve for D from (1), and hence G from (2).

<D=12

<G=118

???

Let's do a check:

From (1)
D+E=90 => 12+78=90 OK
From (2)
D+G=180 => 12+118=130 ≠ 180 ??

Let's solve for G from (2):
D+G=180
12+G=180
12-12+G = 180-12
G=168

Post if it's still not clear.

To find the measures of ∠D and ∠G, we need to understand the concepts of complementary and supplementary angles.

Complementary angles are two angles whose sum is 90 degrees. In this case, <D and <E are complementary, so their sum is 90 degrees.

Supplementary angles are two angles whose sum is 180 degrees. In this case, <D and <G are supplementary, so their sum is 180 degrees.

Given that the measure of ∠E is 78 degrees, we can find the measures of ∠D and ∠G using the following steps:

Step 1: Find the measure of ∠D
Since <D and <E are complementary, their sum is 90 degrees.
∠D + ∠E = 90 degrees
Substituting the given measure of ∠E as 78 degrees:
∠D + 78 degrees = 90 degrees
Subtracting 78 degrees from both sides:
∠D = 90 degrees - 78 degrees
∠D = 12 degrees

Step 2: Find the measure of ∠G
Since <D and <G are supplementary, their sum is 180 degrees.
∠D + ∠G = 180 degrees
Substituting the measure of ∠D we just found as 12 degrees:
12 degrees + ∠G = 180 degrees
Subtracting 12 degrees from both sides:
∠G = 180 degrees - 12 degrees
∠G = 168 degrees

Therefore, the measure of ∠D is 12 degrees and the measure of ∠G is 168 degrees.