Answer:
2) (see image below)
3) x = 8
side(s) = 74
4) x = 10
EF = DE = 67
base = 31
Step-by-step explanation:
For No. 2, if you draw out two triangles with the corresponding angles, you can make it a lot easier. See the image below:
For No. 3, it is given that it's an equilateral triangle, meaning all sides and angles are congruent. So:
12x – 22 = 10x – 6 = 7x + 18
Instead of using all three at once, you can use any two. I'll be using:
12x – 22 = 10x – 6
2x = 16
x = 8
Plugging x in, we can get all the sides, because this is an equilateral triangle:
12x – 22
12(8) – 22
96 – 22
74
For No. 4, it is given that the triangle is an isosceles triangle where DE ≅ EF, so:
8x – 13 = 5x + 17
3x = 30
x = 10
Plugging in x for one of the congruent sides and the base, you can get your needed side length values:
8x – 13
8(10) – 13
80 – 13
67
x + 21
10 + 21
31
