I need help solving these

m∠1 = 140°

m∠2 = 40°

m∠3 = 65°

m∠4 = 75°

m∠5 = 115°

Step-by-step explanation:

We will use a few different methods to find the angles:

A triangle's angles will always add up to 180°. With this information, we can find the last angle of the triangle on the left:

∠1+∠2+∠3=180°

60+80+∠3=180°

Let x represent the value of ∠3. Simplify addition:

Subtract 140 from both sides:

The unknown angle is 40°. With this information, we can find the

m∠1:

m∠1 and the 40° we just found are supplementary angles, which means that their measures will add up to a total of 180°.

∠1+∠2=180°

Insert the value we know:

40°+∠2=180

Let x represent the value of ∠2. Subtract 40 from both sides:

There fore:

m∠1=140°

We can use this same rule to find the m∠2:

∠1+∠2=180°

or, we can use the vertical angles rule. The first angle we found (Which is 40°) is a vertical angle to m∠2, so they have the same value. Therefore:

m∠2=40°

To find m∠3, we need to find the other missing angle in the middle triangle. Use the supplementary angle rule, since the missing angle is supplementary to the angle that is 105°:

∠1+∠2=180°

Insert the known values, substituting x for the unknown angle:

Subtract 105 from both sides:

The unknown angle is 75°. Now find m∠3, knowing that triangles add up to 180°:

m∠2+m∠3+75=180

Insert the m∠2, make m∠3 be x:

Simplify addition:

Subtract 115 from both sides:

Therefore:

m∠3=65°

To find m∠4, use the vertical angle rule.

Therefore:

m∠4=75°

To find m∠5, we could find all triangle measures of the least triangle, or we can use the following:

An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees.

The m∠5 is the exterior angle, and the opposite interior angles are 75° and 40°:

Therefore:

m∠5=115°

:Done

answer: d. $20

step-by-step explanation:

just took the test