Question

geometry with statistics honors - ferraro - 2 - a
topic 4: readiness assessment
d is the midpoint of $overline{ab}$. what is $mangle a$?
a. 22.62
b. 33.69
c. 45
d. 67.38

Explanation:

Step1: Recall triangle - angle sum property

The sum of angles in a triangle is 180°. In right - triangle ACD, we know one angle and want to find ∠A. Since CD is perpendicular to AB and D is the mid - point of AB, triangle ACD is a right - triangle. Let's first consider triangle ACD. We know that ∠ACD=\frac{134.76^{\circ}}{2}=67.38^{\circ} (because CD is the perpendicular bisector of the isosceles triangle ABC, which divides ∠ACB into two equal angles).

Step2: Calculate ∠A

In right - triangle ACD, ∠ADC = 90°. Using the angle - sum property of a triangle (∠A+∠ACD+∠ADC = 180°), we can find ∠A. Substitute ∠ACD = 67.38° and ∠ADC = 90° into the formula: ∠A=180°−90°−67.38° = 22.62°.

Answer:

A. 22.62