Question

1. in the ferris wheel, the measure of ∠efg is 11.25° and the measure of ∠baf is 70°. a. name an example of each of the four types of angles according to their measures in the diagram. b. how many angles are congruent to ∠efg? c. what is the measure of ∠abf? d. what is the measure of ∠cbf?

Explanation:

Step1: Recall angle - type definitions

Acute angle: measure between 0° and 90°. Obtuse angle: measure between 90° and 180°. Right angle: measure of 90°. Straight angle: measure of 180°. $\angle EFG = 11.25^{\circ}$ is an acute - angle example. We can assume a right - angle formed by the vertical and horizontal support of the Ferris - wheel structure (not labeled in the problem but common in such structures). An obtuse - angle example could be an angle formed by two non - adjacent spokes that open wide. The straight angle is $\angle ABC$ (since A, B, and C are collinear).

Step2: Determine congruent angles

The Ferris - wheel is symmetric. If $\angle EFG$ is formed by a certain pattern of spokes, and assuming the Ferris - wheel has 32 equal sections (since $360\div11.25 = 32$), there are 31 other angles congruent to $\angle EFG$ (excluding $\angle EFG$ itself).

Step3: Find $\angle ABF$

In right - triangle ABF, if $\angle BAF = 70^{\circ}$, and the sum of angles in a triangle is 180°, and $\angle AFB = 90^{\circ}$ (assuming the Ferris - wheel's vertical and horizontal supports form right - angles), then $\angle ABF=180^{\circ}-\angle BAF - \angle AFB=180 - 70-90 = 20^{\circ}$.

Step4: Find $\angle CBF$

Since $\angle ABC$ is a straight angle ($180^{\circ}$) and $\angle ABF = 20^{\circ}$, then $\angle CBF=180^{\circ}-\angle ABF = 160^{\circ}$.

Answer:

a. Acute angle: $\angle EFG$, Right angle: (assumed right - angle in the structure), Obtuse angle: (an angle formed by non - adjacent spokes), Straight angle: $\angle ABC$
b. 31
c. $20^{\circ}$
d. $160^{\circ}$