A triangle has one acute angle as the complement of the other. find the third angle
2 answers:
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Answer:
<u>1st pic:</u>
x = 49
top angle = 45
bottom angle = 108
far right angle = 27 degrees
<u>2nd pic:</u>
angle 1 = 88 degrees
angle 2 = 57 degrees
angle 3 = 35 degrees
angle 4 = 145 degrees
Step-by-step explanation:
<u>1st pic:</u>
you can find the far right angle by taking 153 and subtracting it from 180:
⇒ 180 - 153 = 27 degrees
you can find x by the following equation ⇒ x - 4 + 2x + 10 + 27 = 180
combine like terms ⇒ 3x + 33 = 180
subtract 33 from each side ⇒ 3x + 33 - 33 = 180 - 33 ⇒ 3x = 147
divide 3 on each side: ⇒
x = 49
to find the top and bottom angles, substitute 49 for x:
top angle : x - 4
49 - 4 = 45 degrees
bottom angle: 2x + 10
2 x 49 + 10 = 108 degrees
<u>2nd pic:</u>
angle 1:
⇒ 180 - 92 = 88 degrees
angle 2:
⇒ 180 - 123 = 57 degrees
angle 3:
⇒ 180 - (88 + 57) = 35 degrees
angle 4:
⇒ 180 - 35 = 145 dgerees