Answer:
k = 5
Step-by-step explanation:
Given the three angles:
m < (8k + 1)°
m < 90° (assumed that it is a right angle, given the small square by its vertex).
m < 49°
We could simply take the sum of the given angles' measures to solve for the value of k:
(8k + 1)° + 90° + 49° = 180°
Combine the constants:
8k °+ 140° = 180°
Subtract 140° from both sides:
8k° + 140° - 140° = 180° - 140°
8k° = 40°
Divide both sides by 8 to solve for k:
8k°/8° = 40°/8°
k = 5
Verify that we have the correct value for k by substituting 5 into the equation:
(8k + 1)° + 90° + 49° = 180°
[8(5) + 1]° + 90° + 49° = 180°
41° + 90° + 49° = 180°
180° = 180°
Therefore, the correct answer is: k = 5.
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