The measure of angle 1 is (3x + 10º and the measure of what is the measure of angle 7? angle 4 is (4x - 15)
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∠7 = 95°

Step-by-step explanation:

1- getting the value of x:

In the given figure, angle 1 and angle 4 are vertically opposite angles.

Therefore, they are equal in measurement

This means that:

3x + 10 = 4x - 15

4x - 3x = 10 + 15

x = 25

2- getting the value of angle 4:

We know that:

x = 25 and ∠4 is 4x-15

This means that:

∠4 = 4(25) - 15

∠4 = 85°

3- getting the value of ∠6:

From the given figure, we can see that ∠4 and ∠6 are supplement angles, this means that their summation is 180°.

We have calculated that ∠4 is 85°, therefore:

180 = ∠4 + ∠6

∠6 = 180 - ∠4

∠6 = 180 - 85

∠6 = 95°

4- getting the value of angle 7:

From the drawing, we can note that ∠6 and ∠7 are vertically opposite angles. This means that they are equal in measurements.

Therefore:

∠7 = ∠6 = 95°

x is greater than 5

step-by-step explanation:

2x+7 is greater than 17

    -7                           -7

2x is greater than 10

divide by 2 each side

x is greater than 5