Answer:
ACTIVITY 3
\underline{\underline{\bold{Directions:}}}
Directions:
Solve for each angle given the following conditions. Use the figure at the right.
1.) ∠1 = (3y)°, ∠5 = (y + 30)°
Notice in the figure, ∠1 and ∠5 are corresponding angles. So this means that these angles are congruent, and have the same measurement.
\underline{\bold{Solution:}}
Solution:
3y = y + 30
3y - y = 30
2y = 30
y = 30/2
y = 15
Now we've found the value of y. We'll now substitute the value of ∠1 and ∠5.
3y; y = 15
3(15)
45
y + 30
15 + 30
45
Are ∠1 and ∠5 have the same measurement? Yes, both of them have the measure f 45.
\underline{\bold{Answer:}}
Answer:
The value of y is 15.
∠1 = 45°
∠5 = 45°
2.) ∠3 = (2x + 25)°, ∠8 = (5x - 41)°
In the figure, ∠3 and ∠8 are alternate exterior angles. These angles are also congruent, which have the same measurements.
\underline{\bold{Solution:}}
Solution:
2x + 25 = 5x - 41
2x - 5x = 25 + 41
3x = 66
x = 66/3
x = 22
2x + 25; x = 22
2(22) + 25
44 + 25
69
5x - 41
5(22) - 41
110 - 41
69
Are the measures of ∠3 and ∠8 the same? Yes, they're both congruent so that means they have the measurement.
\underline{\bold{Answer:}}
Answer:
The value of x is 22
∠3 = 69°
∠8 = 69°
3.) ∠2 = (3x - 12)°, ∠5 = (x + 8)°
In the figure, ∠2 and ∠5 are same side interior angles. These angles are supplementary.
\underline{\bold{Solution:}}
Solution:
3x - 12 + x + 8 = 180
3x + x - 12 + 8 = 180
4x - 4 = 180
4x = 4 + 180
4x = 184
x = 184/4
x = 46
3x - 12
3(46) - 12
138 - 12
126
x + 8
46 + 8
54
126 + 54 = 180
\underline{\bold{Answer:}}
Answer:
The value of x is 46
∠2 = 126°
∠5 = 54°
4.) ∠2 = (4x - 10)°, ∠6 = (2x + 12)°
In the figure, ∠2 and ∠6 are alternate interior angles. So these angles are congruent as I mentioned earlier that congruent angles have the same measurement.
\underline{\bold{Solution:}}
Solution:
4x - 10 = 2x + 12
4x - 2x = 10 + 12
2x = 22
x = 22/2
x = 11
4x - 10
4(11) - 10
44 - 10
34
2x + 12
2(11) + 12
22 + 12
34
\underline{\bold{Answer:}}
Answer:
The value of x is 11
∠2 = 34°
∠6 = 34°
5.) ∠4 = (x + 5)°, ∠6 = (4x)°
In the figure, ∠4 and ∠6 are also same side interior angles. These angles are supplementary.
\underline{\bold{Solution:}}
Solution:
x + 5 + 4x = 180
5x + 5 = 180
5x = 180 - 5
5x = 175
x = 175/5
x = 35
x + 5
35 + 5
40
4x
4(35)
140
140 + 40 = 180
\underline{\bold{Answer:}}
Answer:
The value of x is 35
∠4 = 40°
∠6 = 140°
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