Answer:
Explanation:
Given:Isosceles triangle ABC with AC as the base.Points D, E, and F are the midpoints of AB, AC, and BC, respectively.Length of BD is 13 inches (BD = 13).Measure of angle BFD (m∠BFD) is 65°.Since D is the midpoint of AB, and E is the midpoint of AC, DE is parallel to BC, and DE is half the length of BC.Since F is the midpoint of BC, BF is equal to FC.Now, let's consider triangle BFD:Angle BDF is equal to angle BFD (both are 65°) since BD and BF are congruent.Angle BDF + Angle BFD + Angle FDB = 180° (Triangle sum property).Let's denote the measure of angle BDF as x. So, we can write the equation:x+65∘+65∘=180∘x+65∘+65∘=180∘Combine like terms:x+130∘=180∘x+130∘=180∘Subtract 130° from both sides:x=50∘x=50∘Now that we know the measure of angle BDF (which is also equal to angle BFD), let's find the measures of other angles in triangle ABC:Angle ABC = 180° - 2 * angle BDF (since ABC is an isosceles triangle)ABC=180°−2∗50∘=80∘ABC=180°−2∗50∘=80∘Angle BAC = (180° - ABC) / 2 (since ABC is isosceles)BAC=(180°−80∘)/2=50∘BAC=(180°−80∘)/2=50∘Now, we have the measures:m∠BDF=m∠BFD=50∘m∠BDF=m∠BFD=50∘m∠ABC=80∘m∠ABC=80∘m∠BAC=50∘m∠BAC=50∘