FIND THE LENGTH OF MP
2 answers:
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Option 3:
m∠ABC = 66°
Solution:
Given and ABH is a transversal line.
m∠FAB = 48° and m∠ECB = 18°
m∠ECB = m∠HCB = 18°
<u>Property of parallel lines: </u>
<em>If two parallel lines cut by a transversal, then the alternate interior angles are equal.</em>
m∠FAB = m∠BHC
48° = m∠BHC
m∠BHC = 48°
<u>Exterior angle of a triangle theorem: </u>
<em>An exterior angle of a triangle is equal to the sum of the opposite interior angles.</em>
m∠ABC = m∠BHC + m∠HCB
m∠ABC = 48° + 18°
m∠ABC = 66°
Option 3 is the correct answer.
<h3>Answer: x = 65.4</h3>
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Work Shown:
cos(angle) = adjacent/hypotenuse
cos(x) = 5/12
x = arccos(5/12)
x = 65.375681647836 which is approximate
x = 65.4 after rounding to one decimal place
Make sure your calculator is in degree mode. The arccosine function is the same as the inverse cosine function (shortened to ).