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9. If [tex]\( m\angle 2 = 7x + 7 \)[/tex], [tex]\( m\angle 3 = 5y \)[/tex], and [tex]\( m\angle 4 = 140 \)[/tex], find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].

A. [tex]\( x = 140, y = 40 \)[/tex]
B. [tex]\( x = 40, y = 140 \)[/tex]
C. [tex]\( x = 8, y = 19 \)[/tex]
D. [tex]\( x = 19, y = 8 \)[/tex]

Sagot :

GinnyAnswer
Sure, let's solve this problem step by step to find suitable values for [tex]\( x \)[/tex] and [tex]\( y \)[/tex].

Given:
1. [tex]\( m42 = 7x + 7 \)[/tex]
2. [tex]\( m3 = 5y \)[/tex]
3. [tex]\( m<4 = 140 \)[/tex]

We need to test the given options to see which one satisfies the two equations [tex]\( m42 = 7x + 7 \)[/tex] and [tex]\( m3 = 5y \)[/tex].

Let's check each option:

### Option 1: [tex]\( x = 140, y = 40 \)[/tex]

- Calculate [tex]\( m42 \)[/tex]:
[tex]\[ m42 = 7x + 7 = 7(140) + 7 = 980 + 7 = 987 \][/tex]
- Calculate [tex]\( m3 \)[/tex]:
[tex]\[ m3 = 5y = 5(40) = 200 \][/tex]

So, for [tex]\( x = 140 \)[/tex] and [tex]\( y = 40 \)[/tex]:
- [tex]\( m42 = 987 \)[/tex]
- [tex]\( m3 = 200 \)[/tex]

### Option 2: [tex]\( x = 40, y = 140 \)[/tex]

- Calculate [tex]\( m42 \)[/tex]:
[tex]\[ m42 = 7x + 7 = 7(40) + 7 = 280 + 7 = 287 \][/tex]
- Calculate [tex]\( m3 \)[/tex]:
[tex]\[ m3 = 5y = 5(140) = 700 \][/tex]

So, for [tex]\( x = 40 \)[/tex] and [tex]\( y = 140 \)[/tex]:
- [tex]\( m42 = 287 \)[/tex]
- [tex]\( m3 = 700 \)[/tex]

### Option 3: [tex]\( x = 8, y = 19 \)[/tex]

- Calculate [tex]\( m42 \)[/tex]:
[tex]\[ m42 = 7x + 7 = 7(8) + 7 = 56 + 7 = 63 \][/tex]
- Calculate [tex]\( m3 \)[/tex]:
[tex]\[ m3 = 5y = 5(19) = 95 \][/tex]

So, for [tex]\( x = 8 \)[/tex] and [tex]\( y = 19 \)[/tex]:
- [tex]\( m42 = 63 \)[/tex]
- [tex]\( m3 = 95 \)[/tex]

### Option 4: [tex]\( x = 19, y = 8 \)[/tex]

- Calculate [tex]\( m42 \)[/tex]:
[tex]\[ m42 = 7x + 7 = 7(19) + 7 = 133 + 7 = 140 \][/tex]
- Calculate [tex]\( m3 \)[/tex]:
[tex]\[ m3 = 5y = 5(8) = 40 \][/tex]

So, for [tex]\( x = 19 \)[/tex] and [tex]\( y = 8 \)[/tex]:
- [tex]\( m42 = 140 \)[/tex]
- [tex]\( m3 = 40 \)[/tex]

After evaluating all the given options, these are the results:

1. [tex]\( (x = 140, y = 40) \)[/tex]: [tex]\( m42 = 987 \)[/tex] and [tex]\( m3 = 200 \)[/tex]
2. [tex]\( (x = 40, y = 140) \)[/tex]: [tex]\( m42 = 287 \)[/tex] and [tex]\( m3 = 700 \)[/tex]
3. [tex]\( (x = 8, y = 19) \)[/tex]: [tex]\( m42 = 63 \)[/tex] and [tex]\( m3 = 95 \)[/tex]
4. [tex]\( (x = 19, y = 8) \)[/tex]: [tex]\( m42 = 140 \)[/tex] and [tex]\( m3 = 40 \)[/tex]

Thus, the option [tex]\( x = 19 \)[/tex] and [tex]\( y = 8 \)[/tex] satisfies the given equations [tex]\( m42 = 7x + 7 \)[/tex] and [tex]\( m3 = 5y \)[/tex]:

- [tex]\( m42 = 140 \)[/tex]
- [tex]\( m3 = 40 \)[/tex]

Therefore, the correct values are:
[tex]\[ \boxed{x = 19, y = 8} \][/tex]
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