Question

Geometry questions....help me someone please

Answer 1

Answer:

Triangle 1: x = 80 degrees, acute

Triangle 2: x = 10 degrees, right

Step-by-step explanation:

Triangle 1:

By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation:

$60 + 40 +x = 180$

Solve for x:

$100 + x = 180\\x = 80$

So, x = 80 degrees

Because all the angles are less than 90 degrees, this is an acute triangle.

Triangle 2:

By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation (with the right angle given):

$3x + 60 + 90 = 180$

Solve for x:

$3x + 150 = 180\\3x = 30\\x = 10$

So, x = 10 degrees

Because there is an angle measuring 90 degrees, this is a right triangle.

Answer 2

Answer:

Triangle 1: x = 80 degrees, acute

Triangle 2: x = 10 degrees, right

By the Sum of Interior Angles Theorem, all the angles inside the triangle adds up to 180 degrees. So, set up this equation:

Solve for x:

So, x = 80 degrees

Because all the angles are less than 90 degrees, this is an acute triangle.

Triangle 2:

By the Sum of Interior Angles Theorem, all the angles inside the triangle add up to 180 degrees. So, set up this equation (with the right angle given):

Solve for x:

So, x = 10 degrees

Because there is an angle measuring 90 degrees, this is a right triangle.