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Find x.
Obtuse
To classify △ DEF we need the angle measures. We can use the information given on the diagram to find x, and knowing x we can find the angle measures.
Multiply parentheses
Add terms
LHS-6x=RHS-6x
LHS+3=RHS+3
Rearrange equation
We now know that x=21. Substituting this value in the expressions, we can find the interior angles at D and at E.
| Angle | Expression | Value |
|---|---|---|
| ∠ D | 4(21)+7 | m∠ D=91 |
| ∠ E | 2(21)+11 | m∠ E=53 |
We can of course use the Triangle Angle Sum Theorem to find the angle at F, but to classify the triangle this is not needed. Notice that m∠ D=91>90, so ∠ D is obtuse. Since the triangle has an obtuse angle, △ DEF is an obtuse triangle.