Respuesta :

Answer: mD=115, mE=49, mF=16

Step-by-step explanation:

DEF is a triangle and were told to find angle measures.

If m∠E is (3F+1) and m∠D is (7F+3)

Use T-angle sum theorem and plug previous terms 7F+3+3F+1+F=180 which give F=16. Then substitute F=16 with angles D and E to find last results.

abidemiokin

The measure of m∠D  is 115 degrees

In the given triangle ∆DEF, if m∠E is one more than three times m∠F, hence;

m∠E = 3m∠F + 1

Similarly, if m∠D is three more than seven times m∠F, then;

m∠D = 7m∠F + 3

Taking the sum of the angles and equate it to 180 degrees

m∠D + m∠E + m∠F = 180

7m∠F + 3 + 3m∠F + 1 + m∠F = 180

11m∠F + 4 = 180

11m∠F = 180-4

11m∠F = 176

m∠F = 16

Since m∠D = 7m∠F + 3

m∠D = 7(16) + 3

m∠D = 115 degrees

Hence the measure of m∠D  is 115 degrees

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