Math / Geometry

QuestionTHIS IS A PRACTICE TEST
10 Mark for Review 480
Triangle $X Y Z$ is similar to triangle $R S T$ such that $X, Y$ , and $Z$ correspond to $R$ , $S$ , and $T$ , respectively. The measure of $\angle Z$ is $20^{\circ}$ and $2 X Y=R S$ . What is the measure of $\angle T$ ? (A) $2^{\circ}$ (B) $10^{\circ}$ (C) $20^{\circ}$ (D) $40^{\circ}$

Studdy Solution

STEP 1

What is this asking? We're told two triangles are similar, given some info about their angles and sides, and asked to find a missing angle. Watch out! Don't mix up corresponding angles and sides!
Similarity means corresponding angles are equal, not necessarily the sides.

STEP 2

1. Match Corresponding Parts
2. Find the Missing Angle

STEP 3

Alright, so we've got these two triangles, triangle $XYZ$ and triangle $RST$ , and they're similar.
That's a magic word in geometry!
It tells us their corresponding angles are equal. $XYZ$ similar to $RST$ means $\angle X$ matches $\angle R$ , $\angle Y$ matches $\angle S$ , and $\angle Z$ matches $\angle T$ .

STEP 4

They also tell us $2XY = RS$ .
This tells us something about the relationship between the side lengths, but we don't need it to find the angles.

STEP 5

We know $\angle Z$ is 20 degrees, and $\angle Z$ corresponds to $\angle T$ .
Because the triangles are similar, corresponding angles are equal.
So, if $\angle Z = 20^\circ$ , then $\angle T$ must also be $\boxed{20^\circ}$ !

STEP 6

The measure of $\angle T$ is $20^\circ$ , so the answer is (C).

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Studdy Solution

STEP 1

What is this asking? We're told two triangles are similar, given some info about their angles and sides, and asked to find a missing angle. Watch out! Don't mix up corresponding angles and sides!
Similarity means corresponding angles are equal, not necessarily the sides.

STEP 2

1. Match Corresponding Parts
2. Find the Missing Angle

STEP 3

STEP 4

They also tell us $2XY = RS$ .
This tells us something about the relationship between the side lengths, but we don't need it to find the angles.

STEP 5

We know $\angle Z$ is 20 degrees, and $\angle Z$ corresponds to $\angle T$ .
Because the triangles are similar, corresponding angles are equal.
So, if $\angle Z = 20^\circ$ , then $\angle T$ must also be $\boxed{20^\circ}$ !

STEP 6

The measure of $\angle T$ is $20^\circ$ , so the answer is (C).

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Studdy Solution

STEP 1

What is this asking? We're told two triangles are similar, given some info about their angles and sides, and asked to find a missing angle. Watch out! Don't mix up corresponding angles and sides!Similarity means corresponding angles are equal, not necessarily the sides.

STEP 2

1. Match Corresponding Parts2. Find the Missing Angle

STEP 3

STEP 4

They also tell us 2XY=RS2XY = RS2XY=RS.This tells us something about the *relationship* between the side lengths, but we don't need it to find the angles.

STEP 5

We know ∠Z\angle Z∠Z is **20 degrees**, and ∠Z\angle Z∠Z corresponds to ∠T\angle T∠T.Because the triangles are similar, corresponding angles are equal.So, if ∠Z=20∘\angle Z = 20^\circ∠Z=20∘, then ∠T\angle T∠T *must also* be 20∘\boxed{20^\circ}20∘​!

STEP 6

The measure of ∠T\angle T∠T is 20∘20^\circ20∘, so the answer is (C).

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We're told two triangles are similar, given some info about their angles and sides, and asked to find a missing angle. Watch out! Don't mix up corresponding angles and sides!
Similarity means corresponding angles are equal, not necessarily the sides.

1. Match Corresponding Parts
2. Find the Missing Angle

They also tell us $2XY = RS$ .
This tells us something about the relationship between the side lengths, but we don't need it to find the angles.

We know $\angle Z$ is 20 degrees, and $\angle Z$ corresponds to $\angle T$ .
Because the triangles are similar, corresponding angles are equal.
So, if $\angle Z = 20^\circ$ , then $\angle T$ must also be $\boxed{20^\circ}$ !

The measure of $\angle T$ is $20^\circ$ , so the answer is (C).