Math  /  Geometry

QuestionQuestion Watch Video Show Examples CNW\triangle C N W can be mapped onto TYE\triangle T Y E by a reflection. If mN=117\mathrm{m} \angle N=117^{\circ}, find mT\mathrm{m} \angle T.
Answer Attempt 1 out of 2 mT\mathrm{m} \angle T \square be determined.
Submit Answer /005e4a159a8a0c010d7d877a3de375c0 Nov 22 11:12

Studdy Solution

STEP 1

What is this asking? If we reflect a triangle CNWCNW to make a new triangle TYETYE, and we know the angle NN is 117117 degrees, what's the angle TT? Watch out! Reflections preserve the size and shape of the triangle, so corresponding angles will be equal!
Don't get tricked by the different labels.

STEP 2

1. Match corresponding angles.
2. Find the measure of angle TT.

STEP 3

Alright, so we've got this triangle CNWCNW becoming triangle TYETYE after a **reflection**.
Imagine flipping a pancake – it's the same pancake, just flipped!
So, the angles in CNWCNW match up with the angles in TYETYE.

STEP 4

The problem tells us that triangle CNWCNW is mapped onto triangle TYETYE.
This means CC matches with TT, NN matches with YY, and WW matches with EE.
So, angle CC corresponds to angle TT, angle NN corresponds to angle YY, and angle WW corresponds to angle EE.

STEP 5

We're given that the measure of angle NN is 117117 degrees.
Since angle NN corresponds to angle YY, we know that mY=mN=117 \mathrm{m}\angle Y = \mathrm{m}\angle N = 117^\circ .

STEP 6

We want to find the measure of angle TT.
Since angle CC corresponds to angle TT, we need to find a connection between angle NN and angle CC.
Unfortunately, we don't have any information about angle CC.
However, we *do* know that angle NN corresponds to angle YY.

STEP 7

Since NN corresponds to YY, and we know mN=117\mathrm{m} \angle N = 117^{\circ}, then mY=117\mathrm{m} \angle Y = 117^{\circ}.
But, this doesn't directly help us find mT\mathrm{m} \angle T.
We're given that CNWCNW maps onto TYETYE, meaning that NN corresponds to YY.
Since we are given mN=117\mathrm{m} \angle N = 117^{\circ}, we know that mY=117\mathrm{m} \angle Y = 117^{\circ}.

STEP 8

The problem states that triangle CNWCNW can be *mapped* onto triangle TYETYE by a reflection.
This means that the corresponding angles are **congruent**, which is a fancy way of saying they have the **same measure**!
Since NN corresponds to YY, we have mN=mY\mathrm{m}\angle N = \mathrm{m}\angle Y.
We're given mN=117\mathrm{m}\angle N = 117^\circ, so mY=117\mathrm{m}\angle Y = 117^\circ.

STEP 9

Since we are looking for mT\mathrm{m}\angle T, and we know that CC corresponds to TT, we need information about mC\mathrm{m}\angle C.
However, the problem only gives us information about mN\mathrm{m}\angle N.
Since reflections preserve angle measures, if NN corresponds to YY, then mN=mY=117\mathrm{m}\angle N = \mathrm{m}\angle Y = 117^\circ.

STEP 10

The problem asks for mT\mathrm{m}\angle T.
Since triangle CNWCNW is reflected onto triangle TYETYE, the angles must match up! CC goes to TT, NN goes to YY, and WW goes to EE.
We're told mN=117\mathrm{m}\angle N = 117^\circ.
Since NN matches with YY, we know mY=117\mathrm{m}\angle Y = 117^\circ.
We want mT\mathrm{m}\angle T.
Since TT matches with CC, we need mC\mathrm{m}\angle C.
We're not given that!
The problem only tells us about angle NN, which corresponds to YY.
Since reflections preserve angle measures, mT\mathrm{m}\angle T cannot be determined from the given information.

STEP 11

mT\mathrm{m} \angle T cannot be determined.

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