Answer:
1. x=9 2. Perimeter= 38 3. 1=70 2=110 3=46 4=102 5=37 4. 1=65 2=25
Step-by-step explanation:
1. To find the value of x, we must first add the lengths of the sides of the triangle, and set them equal to 54.
x+9+2x+3x-9=54
Add like terms
6x=54 x=9
2. Since the triangle is isosceles, 4x=2x+6
4x=2x+6 2x=6 x=3
Substitute the x value in to your sides.
4(3)=12 2(3) +6=12
Add all the sides
12+12+14=38
38 units
3. This one is hard to explain, so sorry if this is confusing.
In order to find Angle 1, we have to find the missing angle of the top triangle, since that angle plus angle 1 = 180 degrees.
To find that angle, add the other 2 angles of that triangle and subtract the sum from 180. 32+38=70 180-70=110
1=70
Angle 2 and Angle 1 also have to add up to 180, since they form a straight line. 180-70=110
Angle 2=110
Now that we know angle 2, we have to find the blank value of the middle triangle. This also shares a straight line with 2, so it equals 70 degrees.
To find 3 we add the angle we just found and 64 degrees, and subtract that from 180. 70+64=134 180-134=46
Angle 3=46
Angle 3, Angle 4, and the 32 degrees angle also add up to 180, so we subtract 32 and 46 from 180 and get 32+46=78
180-78=102
Angle 4= 102
Angle 4, Angle 5, and 41 degrees angle also have to add up to 180. 102+41=143 180-143=37
Angle 5= 37.
4. Right angles have a degree of 90. Add 90 and 25 degrees and subtract from 180. 180-115=65.
Angle 1 =65
The small triangle and the large triangle both have angles of 65 and 90, so therefore they must also both have a 25 degree angle.
Angle 2=25
