Respuesta :

Answer:

Z=80°

Step-by-step explanation:

If the quadrilaterals are similar, they have the same angle measurements.

∠Z=∠F

Since all interior angles of a quadrilateral add up to 360°, we can subtract ∠E, ∠C, and ∠G's measurements from 360°.

360°-100°-120°-60°=∠Z

260°-120°-60°=∠Z

140°-60°=∠Z

80°=∠Z

∠Z=80°

The measure of angle z in quadrilateral ABCD is 80 degrees.

When two quadrilaterals are similar?

Two quadrilaterals are similar quadrilaterals when the three corresponding angles are the same.

What is the sum of the interior angles of a quadrilateral?

The sum of interior angles of a quadrilateral is 360 degrees.

According to the given question

We have two quadrilaterals  ABCD and FECG, and they are similar to each other.

Since, ABCD and FECG are similar to each other.

Therefore, ∠BAD = ∠EFG

⇒ z = ∠EFG

Now, In quadrilateral FECG

We have

∠EFG + 100 + 120 + 60  = 360  

( sum of the interior angles of a quadrilateral is 360 degrees)
⇒ ∠EFG + 280 = 360

⇒ ∠EFG = 360 - 280

⇒ ∠EFG = 80 degrees

Therefore, z = 80 degrees

Learn more about the similar quadrilaterals here:

https://brainly.com/question/16919595

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