Respuesta :

Angle 1 is EQUAL to Angle 4 by definition of vertical angles created by two or more parallel lines cut by a transversal.
So, let's solve for x, first.

3x+10=4x-15

3x+10= 4x-15
-3x        -3x
-----------------
10 = x -15

10= x-15
+15     +15
---------------

25= x

Now, substitute to find angle measures. So, (3*25+10)= (4*25-15). 85 degrees =85 degrees. 

Now, angle 1 is a corresponding angle to angle 5, therefore angle 5 also equals 85 degrees. Angle 5 plus angle 7 sum is 180 degrees because the are supplementary angles.  

Therefore, 85 degrees + unknown angle 7= 180.  180-85= 95 degrees, or the measurement of angle 7. 

The measure of angle 7 is 95 degrees.

c and b are parallel line and are cut by a transversal line a.

Parallel lines cut across by a transversal forms various angles relationship. Examples include corresponding angles, alternate angles etc.

The measure of ∠7 can be found as follows;

∠1 = 3x + 10

∠4 = 4x - 15

Therefore,

∠1 and ∠4 are vertically opposite angles,

Therefore,

3x + 10 = 4x - 15

3x - 4x = -15 - 10

-x = -25

x = 25

Therefore,

∠4 = 4(25) - 15 = 85°

∠1 = 85°

∠1 and ∠5 are corresponding angles.

Therefore,

∠1 ≅∠5

∠5 = 85°

∠5 + ∠7 = 180(angle on a straight line)

85 + ∠7 = 180

∠7 = 180 - 85

∠7 = 95°

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