19) find m∠qrs.

m∠qrs = ______

20) which of the follow is not the name of line below ?

a (overleftrightarrow{ol}) b (overleftarrow{ml})
c (overleftarrow{mo}) d (overrightarrow{lm})

21) solve for x.

x = ______

22) solve for x.

x = ______

23) solve for x.

x = ______

24) solve for x.

-12 + x = 95
+12 +12
x=107

x = 107

Question

19) find m∠qrs.

m∠qrs = ______

20) which of the follow is not the name of line below ?

a (overleftrightarrow{ol})  b (overleftarrow{ml})
c (overleftarrow{mo})  d (overrightarrow{lm})

21) solve for x.

x = ______

22) solve for x.

x = ______

23) solve for x.

x = ______

24) solve for x.

-12 + x = 95
+12        +12
x=107

x = 107

Accepted Answer

### Problem 19: Find $ m\angle QRS $
# Explanation:
## Step 1: Identify the angles at $ R $
The angle $ \angle QRS $ is the sum of $ \angle QRT $ and $ \angle TRS $. Given $ \angle QRT = 30^\circ $ and $ \angle TRS = 32^\circ $.
## Step 2: Add the two angles
To find $ m\angle QRS $, we add the measures of the two angles: $ 30^\circ + 32^\circ $.
$$
30^\circ + 32^\circ = 62^\circ
$$
# Answer:
$ 62^\circ $

### Problem 20: Which is not the name of the line?
# Brief Explanations:
- A line can be named using two points with an arrow (for a ray) or a line segment with two points. But for a line (infinite in both directions), the name should represent the line.
- $ \overleftrightarrow{OL} $, $ \overleftrightarrow{MO} $, $ \overleftrightarrow{LM} $ are valid as they represent the line. $ \overleftrightarrow{ML} $ is a ray (since it has one arrow), not the line. Wait, no—wait, the line is from $ O $ to $ M $ (infinite). Wait, actually, the line is the same as $ LM $, $ OL $, $ MO $. The option $ \overleftrightarrow{ML} $ is a ray (direction matters for rays). Wait, the line is the set of points $ O, L, M $ extended. So the incorrect one is $ \overleftrightarrow{ML} $ (option B) because it's a ray (direction from $ M $ to $ L $, but the line is infinite in both directions, but actually, line names are with two points and arrows. Wait, no—maybe the line is $ \overleftrightarrow{OM} $ or $ \overleftrightarrow{LM} $. Wait, the options: $ \overleftrightarrow{OL} $ (line through $ O $ and $ L $), $ \overleftrightarrow{ML} $ (ray from $ M $ to $ L $, but line would be $ \overleftrightarrow{LM} $ or $ \overleftrightarrow{OL} $ or $ \overleftrightarrow{MO} $. So the answer is B.
# Answer:
B. $ \overleftrightarrow{ML} $

### Problem 21: Solve for $ x $
# Explanation:
## Step 1: Identify the total angle
The angles around a straight line (or a point) sum to $ 180^\circ $. There are 5 angles each of measure $ x^\circ $, so the sum is $ 5x $.
## Step 2: Set up the equation
Since the total angle is $ 180^\circ $, we have $ 5x = 180^\circ $.
## Step 3: Solve for $ x $
Divide both sides by 5:
$$
x = \frac{180^\circ}{5} = 36^\circ
$$
# Answer:
$ 36^\circ $

### Problem 22: Solve for $ x $ in the right triangle
# Explanation:
## Step 1: Recall triangle angle sum
In a triangle, the sum of angles is $ 180^\circ $. The triangle is a right triangle, so one angle is $ 90^\circ $, another is $ 33^\circ $, and the third is $ x^\circ $.
## Step 2: Set up the equation
$$
90^\circ + 33^\circ + x^\circ = 180^\circ
$$
## Step 3: Solve for $ x $
First, add $ 90^\circ $ and $ 33^\circ $: $ 90^\circ + 33^\circ = 123^\circ $. Then subtract from $ 180^\circ $:
$$
x^\circ = 180^\circ - 123^\circ = 57^\circ
$$
# Answer:
$ 57^\circ $

### Problem 23: Solve for $ x $ (parallel lines cut by a transversal)
# Explanation:
## Step 1: Identify the angle relationship
The angle $ x^\circ $ and the $ 35^\circ $ angle are supplementary (they form a linear pair) or corresponding? Wait, the two lines are parallel, cut by a transversal. The $ 35^\circ $ angle and $ x^\circ $ are same - side exterior or interior? Wait, actually, the angle adjacent to $ x^\circ $ is equal to $ 35^\circ $ (corresponding angles), so $ x^\circ + 35^\circ = 180^\circ $? Wait, no—if the lines are parallel, the angle $ x^\circ $ and the $ 35^\circ $ angle are supplementary (linear pair) or equal? Wait, the $ 35^\circ $ angle and the angle adjacent to $ x $ are equal (alternate interior angles). So the angle adjacent to $ x $ is $ 35^\circ $, so $ x + 35 = 180 $ (since they are supplementary).
## Step 2: Solve for $ x $
$$
x = 180 - 35 = 145^\circ
$$
Wait, no—wait, if the two lines are parallel, the $ x^\circ $ and the $ 35^\circ $ angle are same - side interior angles? No, actually, the angle vertical to the $ 35^\circ $ angle is $ 35^\circ $, and $ x^\circ $ and that vertical angle are supplementary. So $ x = 180 - 35 = 145^\circ $.
# Answer:
$ 145^\circ $

### Problem 24: Solve for $ x $ (already solved as $ x = 107 $)
# Explanation:
## Step 1: Given equation
The equation is $ - 12+x=95 $.
## Step 2: Add 12 to both sides
To isolate $ x $, we add 12 to both sides of the equation:
$$
-12 + x+12=95 + 12
$$
$$
x = 107
$$
# Answer:
$ 107 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 19: Find \( m\angle QRS \)

Step 1: Identify the angles at \( R \)

Step 2: Add the two angles

Step 1: Identify the total angle

Step 2: Set up the equation

Step 3: Solve for \( x \)

Answer:

Problem 20: Which is not the name of the line?