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