∠1 and ∠2
are a linear pair. ∡1=x−50
and ∡2=x+32
. Find the measure of each angle. (2 points)
Since ∠1 and ∠2 are a linear pair, their measures add up to 180 degrees.
Therefore, we have the equation:
∠1 + ∠2 = 180
(x-50) + (x+32) = 180
2x - 18 = 180
Adding 18 to both sides:
2x = 198
Dividing both sides by 2:
x = 99
Now we substitute x = 99 into the given expressions to find the measures of ∠1 and ∠2:
∠1 = x - 50 = 99 - 50 = 49 degrees
∠2 = x + 32 = 99 + 32 = 131 degrees
Therefore, the measure of ∠1 is 49 degrees and the measure of ∠2 is 131 degrees.
If T is the midpoint of SU¯¯¯¯¯¯¯
, find x.
(1 point)
x =
To find x, we need to use the fact that T is the midpoint of SU¯¯¯¯¯¯¯.
Since T is the midpoint, it divides the length SU¯¯¯¯¯¯¯ into two equal parts.
Let's assume that the length of ST¯¯¯¯¯¯¯ is x and the length of TU¯¯¯¯¯¯¯ is also x.
So, the length of SU¯¯¯¯¯¯¯ is 2x (ST¯¯¯¯¯¯¯ + TU¯¯¯¯¯¯¯).
Since ST¯¯¯¯¯¯¯ = x and TU¯¯¯¯¯¯¯ = x, we can write the equation:
ST¯¯¯¯¯¯¯ + TU¯¯¯¯¯¯¯ = SU¯¯¯¯¯¯¯
x + x = 2x
2x = 2x
Therefore, x can be any real number, as long as ST¯¯¯¯¯¯¯ and TU¯¯¯¯¯¯¯ have equal values.
We cannot determine the actual value of x without additional information.
To find the measure of each angle, we'll use the fact that the sum of the measures of a linear pair is 180 degrees.
Given that ∡1 = x - 50 and ∡2 = x + 32,
We can set up the equation:
∡1 + ∡2 = 180
Substituting the given values:
(x - 50) + (x + 32) = 180
Simplifying the equation:
2x - 18 = 180
Adding 18 to both sides:
2x = 198
Dividing both sides by 2:
x = 99
Now, we can find the measure of each angle:
∡1 = x - 50 = 99 - 50 = 49 degrees
∡2 = x + 32 = 99 + 32 = 131 degrees
Therefore, the measure of ∡1 is 49 degrees, and the measure of ∡2 is 131 degrees.