Question

Need some clarification about a triangle with three inner triangles that are isosceles

Answer 1

In an isosceles triangles, the base angles are congruent. The sum of the measures of the angles of a triangle is 180. Also, the angles in the middle are 140, 120 and one more. They go around a full circle, so the total is 360 degrees, and you already know 140 and 120.

Answer 2

then would you minus 100 from the other angles to find abc,bca, and cab?

Answer 3

For angle BOA, 360 - 140 - 120 = 100

Answer 4

Now look at triangle ABO. One angle measures 100, the other two angles are congruent and measure x. x + x + 100 = 180

Answer 5

x is the measure of angles ABO and BAO

Answer 6

in my text book its gives an example then the solution i just dont get how they got one part of the solution: (angle)coa =120, then (angle)oca + (angle)oac = 30

Answer 7

Look at the triangle COA. You stated that it is isosceles. In an isosceles triangle, the angles opposite the congruent sides are congruent.

Answer 8

That means that is triangle COA, angles OCA and OAC are congruent and measure the same. You also know that the sum of the measures of all angles of a triangle is 180. Call the measure of angle OCA "y". Then the measure of angle OAC is also "y" because OCA and OAC are congruent. you then have y + y + 120 = 180. SOlve that and you get y = 30

Answer 9

first find angle AOB
120+140 +<AOB=360
so <AOB=100
now for each inner triangle find the other two angles.
For example for triangle AOC, <cao+<aco+<aoc=180
Fill in the known angle. So <cao+<aoc+120=180
<cao+<aoc=180-120=60
since <cao=<aoc
<cao=30=<aoc
Now do the same for the other 2 triangles also. Once all angles are marked, you will add the relevant angles.
In the end you will get <abc=40+20=60
<bca=20+30=50
<cab=30+40=70