Please help - Geometry

For problem 14, (x = 27).    For problem 15, (x = 8)

Step-by-step explanation:

For problem number 14. You realize this is a septagon with 7 angles.

There is a theorem that says the interior sum of the angles equals 180*(number of angles - 2)

So  here  Total sum = 180*(7 - 2) = 180 * 5 = 900 degrees

Add the expressions to get an equation in x.

135 + (5x - 4) + (7x -64) + 120 + (6x - 8) + (4x +15) + (3x + 31) = 900

Simplify:

135 - 4 - 64 + 120 - 8 + 15 + 31 + 5x + 7x + 6x + 4x + 3x = 900

301 - 76 + 25x = 900

225 + 25x = 900

25x = 900 - 225

25x = 675

x = 675/25 =  27.

Problem #15.

Find the other angle supplementary to 71 degrees (the exterior angle)

We get:    180 - 71 = 109 degrees

There are four interior angles here.

The interior sum of these angles is 180*(4 - 2) = 180 * 2 =  360 degrees

(10x +6) + 109 + (8x -1) + (13x - 2) = 360

10x + 8x + 13x  + 6 + 109 -1 - 2 = 360

31x  + 112 = 360

31x = 360 - 112 = 248

x = 248/31 = 8

answer is : muchas/tipicas

have a nice day!

~recklesschicken

9

step-by-step explanation: