The value of x is 54 and the measure of angle 8 is 64 degrees
<h3>How to determine the value of x and find the measure of angle 8?</h3>The given parameters are
Angle 1 = 2x + 10
Angle 8 = x + 10
The figure that completes the question is added as an attachment
From the figure, we have
Angle 1 = Angle 3 ---- vertical angles
Angle 3 + Angle 8 = 180 ---- internal angles within the transversal
Substitute Angle 1 = Angle 3 in the equation Angle 3 + Angle 8 = 180
Angle 1 + Angle 8 = 180
Substitute the known values in the above equation
2x + 8 + x + 10 = 180
Evaluate the like terms
3x = 162
Divide both sides by 3
x = 54
Substitute x = 54 in Angle 8 = x + 10
Angle 8 = 54 + 10
Evaluate
Angle 8 = 64
Hence, the value of x is 54 and the measure of angle 8 is 64 degrees
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In this question , we have to find the value of tan 30 and we need to write the answer in simplified form .
Substituting the values of sin (30) and cos(30, we will get
Multiplying both numerator and denominator by 2, we will get
TO simplify it, we need to multiply both numerator and denominator by square root 3.