There are two probabilities of the solution. First if 80° acts as one of the leg angles, second if 80° acts as the vertex angle.
FIRST PROBABILITY
If 80° is one of the leg angles, then the other angle would be 80° too, because iscosceles has two congruent angles on the leg.
Find the vertex angle
the sum of interior angles in a triangle is 180°
vertex angle + angle on the leg + angle on the leg = 180°
vertex angle + 80° + 80° = 180°
vertex angle + 160° = 180°
vertex angle = 180° - 160°
vertex angle = 20°
The interior angles are 80°,80°,20°
SECOND PROBABILITY
If 80° is the vertex angle, we should find the value of the two leg angles. The two legs has congruent angles.
Find the leg angles
the sum of interior angles in a triangle is 180°
leg angle + leg angle + vertex angle = 180°
2 × leg angle + vertex angle = 180°
2 × leg angle + 80° = 180°
2 × leg angle = 180° - 80°
2 × leg angle = 100°
leg angle = 50°
The interior angles are 80°, 50°, 50°
A dilation is a transformation (notation) that produces an image that is the same shape as the original, but is a different size.
A+s=496
s=496-a
and we are also told that:
s=3a
Since s=s we can say:
3a=496-a add a to both sides
4a=496 divide both sides by 4
a=124
So 124 adult tickets were sold.
-4 1/2, -2 3/8, 1.35, 5.6
Angles in triangle add to 180 degrees
20x=180
x=9
Angle ABC is the top one
8x9=72
