Math / Geometry

Questionometry W. 12 Inscribed angles $98 U$
What is $m \angle T$ ?

Studdy Solution

STEP 1

What is this asking? We need to find the angle inside a circle (an inscribed angle) given an angle at the center of the circle (a central angle) that shares the same arc. Watch out! Don't mix up inscribed angles and central angles!
They have a special relationship, so be careful.

STEP 2

1. Relate the Central Angle to its Intercepted Arc
2. Relate the Inscribed Angle to its Intercepted Arc
3. Calculate the Inscribed Angle

STEP 3

The central angle $\angle UVW$ has a measure of $40^\circ$ .
Central angles are like pizza slices!
The angle of the slice is the same as the arc length along the crust.

STEP 4

So, the intercepted arc $\stackrel{\frown}{UW}$ also measures $40^\circ$ .
That's the piece of the circle's edge between points U and W.

STEP 5

Now, look at the inscribed angle $\angle UTW$ .
It also grabs onto the same arc, $\stackrel{\frown}{UW}$ .

STEP 6

Inscribed angles are half the measure of their intercepted arc.
It's like they're taking a smaller bite out of the same pizza!
This relationship is always true for inscribed angles.

STEP 7

We know the intercepted arc $\stackrel{\frown}{UW}$ measures $40^\circ$ .

STEP 8

The inscribed angle $\angle UTW$ (which is the same as $\angle T$ ) is half of that: $\angle T = \frac{1}{2} \cdot \stackrel{\frown}{UW}$ $\angle T = \frac{1}{2} \cdot 40^\circ$ $\angle T = 20^\circ$

STEP 9

The measure of $\angle T$ is $\bf{20^\circ}$ .

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Questionometry W. 12 Inscribed angles $98 U$
What is $m \angle T$ ?

Studdy Solution

STEP 1

What is this asking? We need to find the angle inside a circle (an inscribed angle) given an angle at the center of the circle (a central angle) that shares the same arc. Watch out! Don't mix up inscribed angles and central angles!
They have a special relationship, so be careful.

STEP 2

1. Relate the Central Angle to its Intercepted Arc
2. Relate the Inscribed Angle to its Intercepted Arc
3. Calculate the Inscribed Angle

STEP 3

The central angle $\angle UVW$ has a measure of $40^\circ$ .
Central angles are like pizza slices!
The angle of the slice is the same as the arc length along the crust.

STEP 4

So, the intercepted arc $\stackrel{\frown}{UW}$ also measures $40^\circ$ .
That's the piece of the circle's edge between points U and W.

STEP 5

Now, look at the inscribed angle $\angle UTW$ .
It also grabs onto the same arc, $\stackrel{\frown}{UW}$ .

STEP 6

Inscribed angles are half the measure of their intercepted arc.
It's like they're taking a smaller bite out of the same pizza!
This relationship is always true for inscribed angles.

STEP 7

We know the intercepted arc $\stackrel{\frown}{UW}$ measures $40^\circ$ .

STEP 8

The inscribed angle $\angle UTW$ (which is the same as $\angle T$ ) is half of that: $\angle T = \frac{1}{2} \cdot \stackrel{\frown}{UW}$ $\angle T = \frac{1}{2} \cdot 40^\circ$ $\angle T = 20^\circ$

STEP 9

The measure of $\angle T$ is $\bf{20^\circ}$ .

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Questionometry W. 12 Inscribed angles 98U98 U98UWhat is m∠Tm \angle Tm∠T ?

Studdy Solution

STEP 1

What is this asking? We need to find the angle inside a circle (an *inscribed* angle) given an angle at the center of the circle (a *central* angle) that shares the same arc. Watch out! Don't mix up inscribed angles and central angles!They have a special relationship, so be careful.

STEP 2

1. Relate the Central Angle to its Intercepted Arc2. Relate the Inscribed Angle to its Intercepted Arc3. Calculate the Inscribed Angle

STEP 3

The **central angle** ∠UVW\angle UVW∠UVW has a measure of 40∘40^\circ40∘.Central angles are like pizza slices!The angle of the slice is the same as the arc length along the crust.

STEP 4

So, the **intercepted arc** UW⌢\stackrel{\frown}{UW}UW⌢ also measures 40∘40^\circ40∘.That's the piece of the circle's edge between points U and W.

STEP 5

Now, look at the **inscribed angle** ∠UTW\angle UTW∠UTW.It also grabs onto the same arc, UW⌢\stackrel{\frown}{UW}UW⌢.

STEP 6

Inscribed angles are *half* the measure of their intercepted arc.It's like they're taking a smaller bite out of the same pizza!This relationship is always true for inscribed angles.

STEP 7

We know the **intercepted arc** UW⌢\stackrel{\frown}{UW}UW⌢ measures 40∘40^\circ40∘.

STEP 8

STEP 9

The measure of ∠T\angle T∠T is 20∘\bf{20^\circ}20∘.

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Questionometry W. 12 Inscribed angles $98 U$
What is $m \angle T$ ?

What is this asking? We need to find the angle inside a circle (an inscribed angle) given an angle at the center of the circle (a central angle) that shares the same arc. Watch out! Don't mix up inscribed angles and central angles!
They have a special relationship, so be careful.

1. Relate the Central Angle to its Intercepted Arc
2. Relate the Inscribed Angle to its Intercepted Arc
3. Calculate the Inscribed Angle

The central angle $\angle UVW$ has a measure of $40^\circ$ .
Central angles are like pizza slices!
The angle of the slice is the same as the arc length along the crust.

So, the intercepted arc $\stackrel{\frown}{UW}$ also measures $40^\circ$ .
That's the piece of the circle's edge between points U and W.

Now, look at the inscribed angle $\angle UTW$ .
It also grabs onto the same arc, $\stackrel{\frown}{UW}$ .

Inscribed angles are half the measure of their intercepted arc.
It's like they're taking a smaller bite out of the same pizza!
This relationship is always true for inscribed angles.

We know the intercepted arc $\stackrel{\frown}{UW}$ measures $40^\circ$ .

The measure of $\angle T$ is $\bf{20^\circ}$ .