In parallelogram TRIG, m∠R = 2x + 19 and m∠G = 4x - 17.
What is m∠T
Opposite angles in a parallelogram are equal, assuming you are following the convention of listing vertices in order, then
4x-17 = 2x+19
2x = 36
x = 18
so angle R = 55°
then angle T = 180-55 = 125°
Well, in the parallelogram TRIG, "T" stands for "Teehee" because it makes me giggle. So, we're trying to find the measure of angle Teehee. Let's call it m∠T.
Now, we know that all the angles in a parallelogram add up to 360 degrees. So, we can write an equation:
m∠R + m∠I + m∠G + m∠T = 360
Substituting the given values, we have:
2x + 19 + x + 4x - 17 + m∠T = 360
Combining like terms, we get:
7x + 2 + m∠T = 360
Now, to isolate m∠T, let's subtract 7x and 2 from both sides:
m∠T = 360 - 7x - 2
So, m∠T is equal to 360 minus 7 times 'x' minus 2.
To find the measure of angle T in parallelogram TRIG, we can use the fact that opposite angles in a parallelogram are congruent. In other words, angle R is congruent to angle G.
So, we have:
m∠R = 2x + 19
m∠G = 4x - 17
Since angle R is congruent to angle G, we can set up an equation:
2x + 19 = 4x - 17
Now, let's solve for x. Subtract 2x from both sides of the equation:
19 = 2x - 17
Add 17 to both sides of the equation:
36 = 2x
Divide both sides of the equation by 2:
18 = x
Now that we know the value of x, we can substitute it back into the equation to find the measure of angle T:
m∠T = 2x + 19
Substituting x = 18 into the equation:
m∠T = 2(18) + 19
m∠T = 36 + 19
m∠T = 55
Therefore, the measure of angle T is 55 degrees.
To find the measure of ∠T in parallelogram TRIG, we can use the fact that the opposite angles in a parallelogram are congruent. In other words, ∠R is congruent to ∠T, and ∠G is congruent to ∠I.
Given that m∠R = 2x + 19 and m∠G = 4x - 17, we can set up the following equation:
2x + 19 = 4x - 17
To solve for x, we need to isolate x on one side of the equation. Let's rearrange the equation:
2x - 4x = -17 - 19
-2x = -36
Now, we can divide by -2 to solve for x:
x = -36 / -2
x = 18
Now that we have the value of x, we can substitute it back into one of the angle measures to find the measure of ∠T. Let's use the equation for ∠R:
m∠R = 2x + 19
Substituting x = 18:
m∠R = 2(18) + 19
m∠R = 36 + 19
m∠R = 55
Therefore, the measure of ∠T is 55 degrees.