Question

If angle 1 and angle 2 form a linear pair, and the m<1= (4x+7) degrees and the m<2= (2x-1) degrees, what is the value of x, and the measure of angle 1 and angle 2?

Answer 1

Answer: The value of x is 29°,  the measure of angle 1 is 123°, and the measure of angle 2 is 57°.

Step-by-step explanation:

A linear pair is the same as a straight line meaning that the sum of the two angles has to equal 180 degrees.

In this case, add both angles and set them to equal to 180 in order to solve for x.

(4x + 7) + (2x-1) = 180   Combine like terms on the left side.

(4x + 2x) + ( 7 - 1) = 180

   6x + 6 = 180   Now subtract 6 from both sides

         -6      -6

    6x = 174    Divide both sides by 6

x = 29  

Since x is  29  degrees we will input it into the expression for the angles and solve for the real value.

m ∠1 = 4(29) + 7

m ∠1  = 116 + 7

m ∠1   = 123  

If the measure of angle 1 is 123 degrees then you can subtract that from  180 to find the measure of angle two or you can use the expression.

m ∠2 = 2(29) -1

m ∠2 = 58 - 1

m ∠2  = 57