1 angle of a triangle measures 12 degrees?

Question

1 angle of a triangle measures 12 degrees. The 2nd angle's measurement is 5 times the third. What is the measure of the third angle?

Answer 1

A triangle has 180 degrees.
We know one angle is 12 degrees.
That leaves 168 degrees.
One angle is five times larger than the other or 168 divided by six sections. (we have one known section plus five unknown sections)
168/6 = 28
So one angle (A) is 12 degrees
the second angle (B) is 28 degrees
the third angle (C) is 168 minus 28 or 140 degrees.

Prove your answer:
5 times 28 equals 140
140 + 28 + 12 = 180

Answer 2

the first thing to think about is that the sum of all the angles in a triangle equals 180. that is if you add all 3 corners then they will add up to 180 regardless of the combination. If it doesn't add to 180 then it cannot be a triangle.

So, lets call these 3 angles a,b & c.

So we know that a + b + c =180.

they tell you that the first angle is 12 and that the second angle is 5 times the size of the third. we can arrange this as follows.

a = 12
b = 5*c
c = ? we don't know yet

rewrite the equation

12 + 5c + c = 180 because we b =5c so we substituted it so we have fewer letters to deal with.

now simplify

12 + 6c =180
6c = 180 -12
6c = 168
c = 168/6
c = 28 degrees

the answer is 28 but don't take it by faith. lets substitude back into the equation just to make sure

12 + 5(28) + 28 =180
12 + 140 + 28 =180
152 +28 =180
180 = 180 checked

Answer 3

Easy as 3.1415926... (can't get enough Pi Day...) 1) Since arc ST = 71, so does the central angle subtending it. The radii to S and T are each perpendicular, so since the angles must add to 360, the angle must add to 109. 2) Using that logic, the angle TRU is 161, so the major arc TSU is 360 minus the other arc (which is 161), or 199. 3) The triangle is circumscribed, so each angle with tangents to the circle has congruent legs. XY is 23 + 7 = 30, YZ is 23 + 56 = 79, so XZ is 56 + 7 = 63.

Answer 4

1st = 12 degrees
2nd = 140 degrees
3rd = 28 degrees

Answer 5

a + b + c = 180
a = 12
b + c = 168
b = 5c

so 5c + c = 168 = 6c

c = 28 degrees