Question

1. be able to solve for x, then find the specified angle measure. find the m\angle lom.
2. how many ways can you name an angle?
3. be able to solve a 45-45-90 special right triangle. formula: \text{hyp} = \sqrt{2} \cdot \text{leg}

find x

Explanation:

Set up the equation for Question 9

Using the Complementary Angles and Angle Addition Postulate knowledge points

$$
LATEXBLOCK0
$$

Solve for x in Question 9

Using the Complementary Angles knowledge point

$$
LATEXBLOCK1
$$

Find the measure of angle LOM

Using the Complementary Angles and Naming Angles knowledge points

$$
LATEXBLOCK2
$$

Determine the ways to name an angle

Using the Naming Angles knowledge point
An angle can be named in 4 ways:

1. By its vertex (if it is the only angle at that vertex).
2. By a number written inside the angle.
3. By three points with the vertex in the middle (e.g., \(\angle LOM\)).
4. By three points in reverse order (e.g., \(\angle MOL\)).

Solve for x in the special right triangle

We are given a \(45^\circ\)-\(45^\circ\)-\(90^\circ\) triangle with hypotenuse \(10\) and legs of length \(x\).
Using the formula \(\text{Hypotenuse} = \sqrt{2} \cdot \text{Leg}\):

$$
LATEXBLOCK3
$$

Answer:

Question 9

\(x = 10\), \(m\angle LOM = 66^\circ\)

Question 10

There are 4 ways to name an angle:

1. By its vertex point (e.g., \(\angle O\)).
2. By a number inside the angle (e.g., \(\angle 1\)).
3. By three points with the vertex in the middle (e.g., \(\angle LOM\)).
4. By three points in reverse order (e.g., \(\angle MOL\)).

Question 11

\(x = 5\sqrt{2}\)