Question

I need help for all of this problems!

Answer 1

1. x = 27°

2. x = 17°

3. m∠1 = 56°

4. m∠2 = 56°

5. m∠3 = 69°

6. m∠1 = 125°

(note at the bottom of answer)

Explanation:

These problems are simple once you know the triangle sum theory and some angle relationships.

1.

To find this missing angle, you need to know that the sum of all angles in a triangle is 180°. Then:

Let the missing angle be x

x = 180 - (80 + 73) --- if we know that the 2 angles combined are 153, we can calculate the third angle

x = 180 - 153

x = 27°

2.

To find the 2 missing angles here, we need to note that this is an isosceles triangle, meaning that 2 of its angles are congruent, and 2 of its sides are congruent. The diagram here shows that the 2 missing angles are congruent, so we can set up an equation like this:

Let the missing angles = x

x =
`(180 - 146)/(2)` --- we can do this because if we know that the angles are the same, we can get their sum by subtracting 146 from 180, then divide it by 2 to get 2 equal angles

x =
`(34)/(2)`

x = 17°

3.

This is the same thing as problem 1.

m∠1 = 180 - (85 + 40)

m∠1 = 180 - 124

m∠1 = 56°

4.

To get the m∠2, we need to know that ∠1 and ∠2 are vertical. Angles are vertical when two straight lines intersect, and they are on opposite sides of the intersection. Vertical angles are congruent.

Now we know that m∠1 and m∠2 are the same.

m∠2 = 56°

5.

To solve for m∠3, use the same method as in problem 1.

m∠3 = 180 - (56 + 55)

m∠3 = 180 - 111

m∠3 = 69°

6.

To solve for this one, we first need to get the angle inside the triangle right next to it.

Let this angle = x

x = 180 - (70 + 55)

x = 180 - 125

x = 55°

With this information, we can now solve for m∠1 because ∠3 and the 55° angle are supplementary. Supplementary angles are angles whose measures add up to 180°, which is a straight line. We can tell that these 2 angles are supplementary because they are both on the same side of a transversal on the shared intersection point. To solve for m∠1, we do this:

m∠1 = 180 - 55 --- 55 is the known supplementary angle to m∠1

m∠1 = 125°

That should be everything you need to know to complete the worksheet, comment here if you need more help or if i missed something.