Answer:
3. 37°, 37°, and 106°
Step-by-step explanation:
I am doing #3 as shown in the picture.
Isosceles triangle is a triangle with 2 sides same and their opposite angles same. Those angles are congruent and called base angles. The remaining angle is the vertex angle.
We let each of the base angles as "b" and the vertex angle as "v".
Now,
Vertex Angle is 5 less than 3 times one of the base angles, we can write:
[tex]v = 3b - 5[/tex]
We also know that 3 angles in a triangle add up to 180 degrees, so we can write:
v + b + b = 180
v + 2b = 180
(3b - 5) + 2b = 180
We have replaced "v" with the first equation and created an equation in "b". So now we can solve for b:
[tex](3b - 5) + 2b = 180\\3b-5+2b=180\\5b=180+5\\5b=185\\b=\frac{185}{5}\\b=37[/tex]
Now, finding v:
v = 3b - 5
v = 3(37) - 5
v = 106
Thus, the three angles of the triangle are:
37°, 37°, and 106°
