Given that the m < 60° and m < (8y — 2) add up to 90° because they are complementary angles:
We could simply establish the following formula to solve for y:
m < 60° + m < (8y — 2)° = 90°
60° + 8y — 2 = 90°
58° + 8y = 90°
Subtract 58° from both sides
58° — 58° + 8y = 90° — 58°
8y = 32°
Divide both sides by 8:
8y/8 = 32°/8
y = 4
Therefore, the value of y = 4°
Double check whether we derived with the correct answer:
m < 60° + m < (8y — 2)° = 90°
m < 60° + m < 8 (4)— 2° = 90°
m < 60° + m < 32 ° — 2° = 90°
m < 60° + m < 30° = 90°
m < 90° = 90° (True statement). Thus, we have the correct value for y.
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