Math / Geometry

QuestionThe figure above shows quadrilateral WXYZ. What is the measure of $\angle Z$ ? (A) $45^{\circ}$ (B) $120^{\circ}$ (C) $135^{\circ}$ (D) $145^{\circ}$ (E) $225^{\circ}$

Studdy Solution

STEP 1

What is this asking? We need to find the missing angle inside a four-sided shape, given the other three angles. Watch out! Don't forget all the angles in a quadrilateral always add up to a specific number!

STEP 2

1. Sum of Angles in a Quadrilateral
2. Calculate the Missing Angle

STEP 3

Alright, let's break this down!
We know that the angles inside any quadrilateral always add up to $360^\circ$ .
This is a fundamental fact in geometry, so let's keep it in mind!

STEP 4

We're given three angles: $\angle W = 55^\circ$ , $\angle X = 110^\circ$ , and $\angle Y = 60^\circ$ .
Let's call our missing angle $\angle Z$ .

STEP 5

Since all the angles add up to $360^\circ$ , we can write this as an equation: $\angle W + \angle X + \angle Y + \angle Z = 360^\circ$

STEP 6

Now, let's plug in the values we know: $55^\circ + 110^\circ + 60^\circ + \angle Z = 360^\circ$

STEP 7

Let's add those angles together: $225^\circ + \angle Z = 360^\circ$

STEP 8

To find $\angle Z$ , we need to isolate it.
We can do this by subtracting $225^\circ$ from both sides of the equation: $225^\circ - 225^\circ + \angle Z = 360^\circ - 225^\circ$ $\angle Z = 135^\circ$

STEP 9

So, the measure of $\angle Z$ is $\bf{135^\circ}$ !
That's answer choice (C)!

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QuestionThe figure above shows quadrilateral WXYZ. What is the measure of $\angle Z$ ? (A) $45^{\circ}$ (B) $120^{\circ}$ (C) $135^{\circ}$ (D) $145^{\circ}$ (E) $225^{\circ}$

Studdy Solution

STEP 1

What is this asking? We need to find the missing angle inside a four-sided shape, given the other three angles. Watch out! Don't forget all the angles in a quadrilateral always add up to a specific number!

STEP 2

1. Sum of Angles in a Quadrilateral
2. Calculate the Missing Angle

STEP 3

Alright, let's break this down!
We know that the angles inside any quadrilateral always add up to $360^\circ$ .
This is a fundamental fact in geometry, so let's keep it in mind!

STEP 4

We're given three angles: $\angle W = 55^\circ$ , $\angle X = 110^\circ$ , and $\angle Y = 60^\circ$ .
Let's call our missing angle $\angle Z$ .

STEP 5

Since all the angles add up to $360^\circ$ , we can write this as an equation: $\angle W + \angle X + \angle Y + \angle Z = 360^\circ$

STEP 6

Now, let's plug in the values we know: $55^\circ + 110^\circ + 60^\circ + \angle Z = 360^\circ$

STEP 7

Let's add those angles together: $225^\circ + \angle Z = 360^\circ$

STEP 8

To find $\angle Z$ , we need to isolate it.
We can do this by subtracting $225^\circ$ from both sides of the equation: $225^\circ - 225^\circ + \angle Z = 360^\circ - 225^\circ$ $\angle Z = 135^\circ$

STEP 9

So, the measure of $\angle Z$ is $\bf{135^\circ}$ !
That's answer choice (C)!

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QuestionThe figure above shows quadrilateral WXYZ. What is the measure of ∠Z\angle Z∠Z ? (A) 45∘45^{\circ}45∘ (B) 120∘120^{\circ}120∘ (C) 135∘135^{\circ}135∘ (D) 145∘145^{\circ}145∘ (E) 225∘225^{\circ}225∘

Studdy Solution

STEP 1

What is this asking? We need to find the missing angle inside a four-sided shape, given the other three angles. Watch out! Don't forget all the angles in a quadrilateral *always* add up to a specific number!

STEP 2

1. Sum of Angles in a Quadrilateral2. Calculate the Missing Angle

STEP 3

Alright, let's break this down!We know that the angles inside *any* quadrilateral always add up to 360∘360^\circ360∘.This is a fundamental fact in geometry, so let's keep it in mind!

STEP 4

We're given three angles: ∠W=55∘\angle W = 55^\circ∠W=55∘, ∠X=110∘\angle X = 110^\circ∠X=110∘, and ∠Y=60∘\angle Y = 60^\circ∠Y=60∘.Let's call our missing angle ∠Z\angle Z∠Z.

STEP 5

Since all the angles add up to 360∘360^\circ360∘, we can write this as an equation: ∠W+∠X+∠Y+∠Z=360∘ \angle W + \angle X + \angle Y + \angle Z = 360^\circ ∠W+∠X+∠Y+∠Z=360∘

STEP 6

Now, let's **plug in** the values we know: 55∘+110∘+60∘+∠Z=360∘ 55^\circ + 110^\circ + 60^\circ + \angle Z = 360^\circ 55∘+110∘+60∘+∠Z=360∘

STEP 7

Let's **add** those angles together: 225∘+∠Z=360∘ 225^\circ + \angle Z = 360^\circ 225∘+∠Z=360∘

STEP 8

STEP 9

So, the measure of ∠Z\angle Z∠Z is 135∘\bf{135^\circ}135∘!That's answer choice (C)!

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Start learning now

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QuestionThe figure above shows quadrilateral WXYZ. What is the measure of $\angle Z$ ? (A) $45^{\circ}$ (B) $120^{\circ}$ (C) $135^{\circ}$ (D) $145^{\circ}$ (E) $225^{\circ}$

What is this asking? We need to find the missing angle inside a four-sided shape, given the other three angles. Watch out! Don't forget all the angles in a quadrilateral always add up to a specific number!

1. Sum of Angles in a Quadrilateral
2. Calculate the Missing Angle

Alright, let's break this down!
We know that the angles inside any quadrilateral always add up to $360^\circ$ .
This is a fundamental fact in geometry, so let's keep it in mind!

We're given three angles: $\angle W = 55^\circ$ , $\angle X = 110^\circ$ , and $\angle Y = 60^\circ$ .
Let's call our missing angle $\angle Z$ .

Since all the angles add up to $360^\circ$ , we can write this as an equation: $\angle W + \angle X + \angle Y + \angle Z = 360^\circ$

Now, let's plug in the values we know: $55^\circ + 110^\circ + 60^\circ + \angle Z = 360^\circ$

Let's add those angles together: $225^\circ + \angle Z = 360^\circ$

So, the measure of $\angle Z$ is $\bf{135^\circ}$ !
That's answer choice (C)!