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atroni [7]
3 years ago
11

How do I find these angle measures?

Mathematics
2 answers:
ch4aika [34]3 years ago
6 0
The measure of angle 1 is 75 degrees because it is a corresponding angle with the one given of 75 degrees
the measure of angle 2 is 105 degrees because it forms a supplementary angle with the one next to it that is 75 degrees. (this means they add up to 180 degrees.
sweet-ann [11.9K]3 years ago
4 0
M∡1 = 75° because when parallel lines are cut by a transversal, corresponding angles are congruent

m∡2 = 180° - 75° = 105° because when adjacent angles form a straight angle (linear pair) they are supplementary 
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Step-by-step explanation:

Notice that the wall and the floor make a right angle, and the ladder lining against the wall makes the hypotenuse of a right angle triangle.

See the attached image for explanation, and for the angle \theta that we are trying to find, which is formed between the ladder and the wall.

Notice as well that the 8 ft section of the wall, is an "adjacent" side of the angle \theta , and that the 5 ft segment between the wall and the base of the ladder is the "opposite" side to the angle.

We can then use the "tangent" of the angle \theta  which is defined as the quotient between the opposite side divided the adjacent side to investigate  the measure of the angle \theta . We will use the "arctangent" to solve for the angle:

tan(\theta)= \frac{opposite}{adjacent} \\tan(\theta)= \frac{5}{8}\\tan(\theta)=0.625\\\theta=arctan(0.625)\\\\\theta=32.00538

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