Question

If m<2= x m<3=40 and m<4 = 5x +14 what is m<1?

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121

Answer 1

To find the measure of angle 1, you can set up an equation based on the fact that the sum of all the angles in a quadrilateral is 360 degrees.

Since angle 2, 3, and 4 are given, you can find their measures:

m<2 = x
m<3 = 40
m<4 = 5x + 14

Now, add the measures of these angles and set it equal to 360 degrees:

x + 40 + (5x + 14) + m<1 = 360

Combine like terms:
6x + 54 + m<1 = 360

Subtract 54 from both sides:
6x + m<1 = 306

Since m<1 + m<4 = 180 (angles 1 and 4 form a linear pair), you can substitute m<4 = 5x + 14 into the equation above:

6x + m<1 = 306
6x + 5x + 14 = 306
11x + 14 = 306
11x = 292
x = 26.545

Now, substitute x back into the equation for m<1:

6(26.545) + m<1 = 306
159.3 + m<1 = 306
m<1 = 146.7

Therefore, m<1 = 147 degrees.

None of the answer options provided are correct.