Answer:
<em>The measure of angle A is 73°</em>
Step-by-step explanation:
<u>Isosceles Triangles</u>
An isosceles triangle is a triangle with exactly two congruent sides. The angles the congruent sides form with the third side are also equal.
The triangle ABC is isosceles and AB congruent with BC. The angle at B measures 34°.
The other two angles are congruent, i.e. their measures are the same. Since the internal angles of a triangle sum 180°:

Thus:

The measure of angle A is 73°
The length of the daylight was 9 hr 10 min
Given
base=2x+6
height=x+4
and
area=56 square units
56=1/2 times (2x+6) times (x+4)
times bot sides by 2
112=(2x+6)(x+4)
expand
112=2x²+14x+24
divide both sides by 2
56=x²+7x+12
minus 56 both sides
0=x²+7x-44
factor
waht 2 numbers mulitply to get -44 and add to get 7
11 and -4
0=(x-4)(x+11)
set to 0
x-4=0
x=4
x+11=0
x=-11
false, measures can't be negative
x=4
height=x+4
height=4+4=8
base=2x+6
base=2(4)+6=8+6=14
x=4 and base=14 and height=8
15/x=75/100
15/x=3/4
times 4x both sides
4*15=3x
60=3x
divide both sides by 3
20=x