Angle E = 97° and Angle D = 83°
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Supplementary angles add to equal 180°. If angle D is 14° less than angle E, we know the sum must be 180 and will use it to solve for the unknowns.
Given:
Angle E - 14° = Angle D
Angle E + Angle D = 180
I’m going to solve this like a system of two equations ^ from above. To shorten it I’m just going to write E and D rather than “angle E, angle D.”
Since E - 14 = D, then E = D + 14 must be true.
This can be substituted (for E) into the second equation I made for the system:
D + 14 + D = 180
Simplify: 2(D) + 14 = 180
Subtract 14 from both sides:
2D = 166
Divide both sides by 2:
D = 83
Angle D measures 83°.
What is 14° more than 83°? 97°. Angle E must measure 97°. To check, add them to verify they have a sum of 180 degrees: 83 + 97 = 180. True!
Measurements:
Angle E = 97°
Angle D = 83°