Math / Geometry

QuestionThese figures are congruent. What is $m \angle V$ ?

Studdy Solution

STEP 1

1. Congruent figures have corresponding angles that are equal.
2. The given polygons are congruent, meaning each angle in one polygon corresponds to an angle in the other polygon.
3. We need to find the measure of $m \angle V$ in polygon $UTSV$ .

STEP 2

1. Identify corresponding angles.
2. Calculate the measure of the unknown angle.

STEP 3

Identify the corresponding angles between the two polygons. Since the polygons are congruent, the angles in polygon $GHIF$ correspond to the angles in polygon $UTSV$ . Match the angles based on their positions in the polygons.

STEP 4

Determine which angle in polygon $GHIF$ corresponds to $\angle V$ in polygon $UTSV$ . Since the polygons are congruent, we can use the given angles to find the corresponding angles.

STEP 5

From the given information: - $\angle G$ in $GHIF$ corresponds to $\angle U$ in $UTSV$ (both are $88^\circ$ ). - $\angle H$ in $GHIF$ corresponds to $\angle T$ in $UTSV$ (both are $115^\circ$ and $127^\circ$ respectively, indicating a mistake in the problem statement or image description). - $\angle I$ in $GHIF$ corresponds to $\angle S$ in $UTSV$ (both are $30^\circ$ ).
Since $\angle V$ is the remaining angle in polygon $UTSV$ , it corresponds to the remaining angle in polygon $GHIF$ .

STEP 6

Calculate the measure of $\angle V$ by using the corresponding angle from polygon $GHIF$ . Since $\angle F$ is the remaining angle in polygon $GHIF$ , it corresponds to $\angle V$ .

STEP 7

Calculate $m \angle F$ in polygon $GHIF$ using the sum of angles in a polygon. The sum of the interior angles of a quadrilateral is $360^\circ$ .
$m \angle G + m \angle H + m \angle I + m \angle F = 360^\circ$
Substitute the known angles:
$88^\circ + 115^\circ + 30^\circ + m \angle F = 360^\circ$

STEP 8

Solve for $m \angle F$ :
$233^\circ + m \angle F = 360^\circ$
$m \angle F = 360^\circ - 233^\circ$
$m \angle F = 127^\circ$
The measure of $m \angle V$ is:
$\boxed{127^\circ}$

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