The value of y is 36
The value of w is -13
<h3>Calculating the value of angles </h3>
From the given question, we are to determine the value of y
From the given information,
We have that line b is parallel to line c
Then,
74° + (2y + 34)° = 180°
Solve for y
(2y + 34)° = 180° - 74°
2y° + 34° = 106°
2y° = 106° - 34°
2y° = 72°
y° = 72°/2
y° = 36°
Hence, y = 36
In the second diagram,
72° + ∠ACB + ∠BCD = 180° (<em>Sum of angles on a straight line</em>)
From the given information,
BC bisects ∠ACD
Thus,
∠ACB = ∠BCD
Then, we can write that
72° + ∠BCD + ∠BCD = 180°
72° + 2 × ∠BCD = 180°
2 × ∠BCD = 180° - 72°
2 × ∠BCD = 108°
∠BCD = 108°/2
∠BCD = 54°
Since line j is parallel to line k
Then,
(2w + 80)° = ∠BCD (<em>Corresponding angles</em>)
(2w + 80)° = 54°
2w° + 80° = 54°
2w° = 54° - 80°
2w° = -26°
w° = -26°/2
w° = -13°'
Hence, w = -13
Learn more on Calculating the value of angles here: brainly.com/question/21369105
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