Answer:

The sum of 2 consecutive interior angles is equal its opposite exterior angle.

The 2 consecutive interior angles are:

25° and (x - 15)°

and its opposite exterior angle is:

(3x - 10)°

So we can equate it as:

25  + (x - 15) = (3x - 10)

solve for x,

25 + x - 15 = 3x - 10

10 + x = 3x - 10

3x - x = 10 + 10

2x = 20

x = 20/2

x = 10

Solve for the missing exterior angle,

3x - 10

= 3(10) - 10

= 30 - 10 = 20° ---> looks kind of small!

Solve for the missing interior angle,

x - 15

= 10 - 15 = -5   ---> OOOPSSS

Something is wrong with the givens or you missed some information or conditions!

PROOF THE GIVENS ARE WRONG:

Assuming the external angle is correct at 20°, then its supplementary angle is 180° - 20° = 160°.

This 160° is one of the interior angles of the triangle.

So now we know 2 interior angles as 25° and 160°, so the third interior angles must be:

180 - 25 - 160 = -5°

The answer of the 3rd interior angle is negative 5°, which is not a possible answer!

TIP TO MAKE THE GIVENS TRUE, THE (x-15)° SHOULD BE (x+15)°,

Let's solve it using (x+15)°

25  + (x + 15) = (3x - 10)

40 + x = 3x -10

2x = 50

x = 25

Solve for the missing exterior angle,

3x - 10

= 3(25) - 10

= 75 - 10

= 65°

Knowing external angle is 65°, its supplementary is 180 - 65 = 115°.

So the 115° is one of the internal angles of the triangle.

Solve for the missing interior angle,

x + 15

= 25 + 15

= 40°

Now let's check if sum of interior angles of the triangle is equal to 180°.

25° + 40° + 115° = 180°

180° = 180°    ✔✔✔ TRUE

So there you go, we are able to solve it as long as the given is corrected from (x-15)° to (x+15)°

✓✓✓ Press that brainliest button if this was helpful. ✓✓✓

• • •  Follow for more math solutions and fun facts! • • •