Answer:
∠a = 60°
∠b = 60°
∠c = 120°
∠d = 60°
Step-by-step explanation:
I have a couple things attached that should help. In the first attachment I've assigned all the angles with their congruent counterparts. I've also assigned the value 60 degrees with a (z) to help visualize all the degrees that are 60 degrees.
So first of all we can deduce that the angles represented by z up in the far left corner equal 60 degrees. We notice that the four angles that make up the intersection in that corner equal 360 degrees total. So we can find the angles of the other two mystery angles by adding 60+60.
60/60 = 120
120 is the sum of two of the angles. We need 2 more. We know that the remaining two angles are congruent, due to just two lines being intersected. Thus, we can subtract 120 from 360 and get the sum of those two angles.
360-120 = 240
Divide by 2, to get the degrees of each individual angle.
240/2 = 120
So two angles in the upper left-hand corner are 60 degrees, and the other two congruent angles are 120 degrees. This can be seen in the second attachment.
Now we can solve for almost the rest of the angles. Notice the triangle that angles a, b, and the inside corner in the upper left hand corner make. We know that a triangle has 180 degrees. We also know that one angle is 60 degrees.
180-60 = 120
Divide by two to get the degrees of each individual angle.
120/2 = 60
Both ∠a and ∠b are 60°
Next, because we know ∠b is 60 degrees, we also know that b's reflectory angle equals 60 degrees. Since there are six angles in the lower middle angle, we can add up the four angles we already know to begin to solve for ∠d. We will be using the value 2d to represent ∠d and its congruent angle as they both have the same measurement of degrees.
60+60+60+60+2d = 360
240 + 2d = 360
2d = 120
d = 60
∠d and its congruent angle both equal 60°
We're almost done! Since we know that both ∠a (that we now know it is 60 degrees) and ∠c rest on a straight line, we know that the sum of both ∠a and ∠c is going to equal 180°.
60+c = 180
Subtract 60 from 180 to get c.
∠c = 120
Hope this helped!
