Solve for the value of y and the measures of angles 1 and 3.
m angle 1=(10y+2)
m angle 3=(12y-8)
Since there is no INFO that shows the relationship between angles 1 and 3,
i'm going to assume they are equal:
10y + 2 = 12y - 8,
10y - 12y = -8 - 2,
-2y = -10,
y = 5.
10y + 2 = 10*5 + 2 = 52 deg.
12y - 8 = 12*5 - 8 = 52 deg.
(12x-15)=(3x+45)
To solve for the value of y and the measures of angles 1 and 3, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Given:
m angle 1 = 10y + 2
m angle 3 = 12y - 8
Step 1: Set up an equation using the sum of the angles in a triangle:
m angle 1 + m angle 3 + m angle 2 = 180
Step 2: Substitute the given angles into the equation:
(10y + 2) + (12y - 8) + m angle 2 = 180
Step 3: Simplify the equation:
22y - 6 + m angle 2 = 180
Step 4: Rearrange the equation to solve for m angle 2:
m angle 2 = 186 - 22y
Now we have two equations:
m angle 1 = 10y + 2
m angle 2 = 186 - 22y
To solve for y, we need to set m angle 1 equal to m angle 2 and solve for y.
Step 5: Set m angle 1 equal to m angle 2:
10y + 2 = 186 - 22y
Step 6: Simplify and solve for y:
10y + 22y = 186 - 2
32y = 184
y = 184/32
y = 5.75
Therefore, the value of y is 5.75.
Step 7: Substitute the value of y back into the original equations to find the measures of angles 1 and 3:
m angle 1 = 10(5.75) + 2
m angle 1 = 57.5 + 2
m angle 1 = 59.5
m angle 3 = 12(5.75) - 8
m angle 3 = 69 - 8
m angle 3 = 61
So, the measures of angles 1 and 3 are 59.5 degrees and 61 degrees, respectively.