Question

for exercises 6 - 8, use the diagram to determine the measures of the given angles. angles bfd and afe are right angles. 6. m∠bfc 7. m∠gfa 8. m∠efd

Explanation:

Step1: Recall right - angle property

Since $\angle BFD = 90^{\circ}$ and $\angle DFC=50^{\circ}$, and $\angle BFC+\angle DFC=\angle BFD$.

Step2: Calculate $\angle BFC$

$m\angle BFC=m\angle BFD - m\angle DFC$. Substituting the values, we get $m\angle BFC = 90^{\circ}-50^{\circ}=40^{\circ}$.

Step3: Recall vertical - angle property

$\angle GFA$ and $\angle EFB$ are vertical angles. Also, $\angle EFB+\angle BFD+\angle DFE = 180^{\circ}$, and $\angle DFE = 90^{\circ}$, $\angle BFD = 90^{\circ}$, so $\angle EFB = 0^{\circ}$, then $m\angle GFA=0^{\circ}$.

Step4: Recall right - angle property for $\angle EFD$

Since $\angle AFE = 90^{\circ}$, and $\angle EFD$ and $\angle AFE$ are part of a straight - line at point $F$, $m\angle EFD = 90^{\circ}$.

Answer:

1. $m\angle BFC = 40^{\circ}$
2. $m\angle GFA = 0^{\circ}$
3. $m\angle EFD = 90^{\circ}$