Question

∠1 and ∠2
are a linear pair. ∡1=x−50
and ∡2=x+32
. Find the measure of each angle. (2 points)

Answer 1

If T is the midpoint of SU¯¯¯¯¯¯¯
, find x.



(1 point)
x =

Answer 2

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.

Answer 3

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.