M∠P is 10 more than 3 times a number, m∠N is 8 less than 5 times the same number. What is m∠M?
1 answer:
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Answer:
See explanation
Step-by-step explanation:
<u><em>1st photo:</em></u>
x =
= 15
x =
<u><em>2nd photo:</em></u>
(a) GEH ~ FGH ~ FEG
<em>similar triangles, use similar corners in the right order</em>
(b) AND
<em>similar triangles, use similar sides in proportion</em>
<em />
<u><em>3rd photo:</em></u>
x = 4.5 or 4 1/2
<em>2x = 9</em>
<em>x = 4.5 or 4 1/2</em>
<em />
<u><em>4th photo:</em></u>
Length of string = 118.2 ft
<em>sin(40) = 76/x</em>
<em>x = 76/sin(40) = 118.2</em>
Answer:
m∠1 + m∠3 = m∠2 + m∠4
Step-by-step explanation:
In the figure attached,
In the given trapezoid if two sides AB and CD are parallel and AD is a transverse,
m∠1 + m∠3 = 180°
Similarly, if AB and CD are parallel and BC is a transverse,
m∠2 + m∠4 = 180°
Therefore, m∠1 + m∠3 = m∠2 + m∠4 is the relation between these angles.
