Question

ihg ≅ stuv. what is m∠t?

Explanation:

Step1: Recall angle - sum property of quadrilaterals

The sum of the interior angles of a quadrilateral is 360°.

Step2: Identify corresponding angles

Since quadrilateral IHFG ≅ quadrilateral STUV, ∠H corresponds to ∠T, ∠I corresponds to ∠V, ∠F corresponds to ∠S, and ∠G corresponds to ∠U.

Step3: Calculate m∠T

We know that for quadrilateral STUV, we can find m∠T using the angle - sum formula. Let m∠T=x. Then x + 83°+128° + ∠U=360°. For quadrilateral IHFG, the sum of its angles is also 360°. Since the quadrilaterals are congruent, we can also calculate as follows:
The sum of the known angles in quadrilateral IHFG is 41° + 108°=149°.
For quadrilateral STUV, we know two angles 83° and 128°. Let's use the angle - sum of a quadrilateral formula:
m∠T=360°-(83° + 128°+ ∠U). Since the quadrilaterals are congruent, we can find the missing angle in quadrilateral IHFG first. The sum of the angles in quadrilateral IHFG: 41°+108° + ∠F+ ∠G = 360°.
We know that for congruent quadrilaterals, the corresponding angles are equal.
The sum of the known angles in quadrilateral STUV is 83°+128° = 211°.
m∠T=360°-(83° + 128°+ ∠U). Since the quadrilaterals are congruent, we can also calculate the missing angle in quadrilateral IHFG and use the correspondence.
In quadrilateral IHFG, if we consider the sum of angles: 41°+108°+ ∠F+ ∠G = 360°.
For congruent quadrilaterals, m∠T = 41°.

Answer:

41