Daily Warm-Up Quiz #2CONJECTURES: Complete each conjecture below. (2 TOTAL POINTS; ½ POINT EACH)1. If two angles are a linear pair of angles, then the angles are _____________________ (____). (LINEAR PAIR CONJECTURE)

2. If two angles are vertical angles, then the angles are ________________________________. (VERTICAL ANGLES CONJECTURE)

3. If two angles are both equal in measure and supplementary, then each angle measures _____.(EQUAL SUPPLEMENTS CONJECTURE)

4. The sum of the measures of the interior angles of any triangle is ________________________. (TRIANGLE SUM CONJECTURE)

DIRECTIONS: Translate the f ollowing sentences into algebraic equations on the lines

provided:

1. The supplement of an angle is 20 less than the angle. (1)

2. The complement of an angle is 10 more than the angle. (3)

3. Five times the supplement of an angle is 630 more than it complement. (10)

4. Twenty more than the supplement of an angle is three times its complement.

(11)

For all problems below,

Let m = missing angle’s measure

Let 90- m = angle’s complement

Let 180- m = angle’s supplement

DO NOT SOLVE! DO NOT SOLVE! DO NOT SOLVE! DO NOT SOLVE!

SOLVE THE FOLLOWING:

5(180-M) = (90-M) + 630 (180-M) + 20 =3 (90-M)

BASIC ALGEBRA REVIEW

Define the following before translating the following sentences to mathematical equations in 6-7 below (1 POINT; ALL OR NONE)

Let __________ = the measure of an unknown angle Let __________ = the angle’s complement Let__________ = the angle’s supplement

2 TOTAL POINTS; 1 POINT EACH

Angle’s measure is one-third its supplement

Supplement is 6 degrees more than four times its complement

Algebra Connection: Vertical Angles & Linear Pairs

COMPLETE THE CHART BELOW:

n n-gon 7 dodecagon

Use the angle relationships in the diagrams below to solve for the given variable in each diagram below. Show ALL work!

a. x = ______ b. x = _____ c. x = ______

Applications1. : A company is manufacturing a gear that has the shape of a regular

polygon. The measure of each angle of the gear is 162. How many sides does the

gear have?

2. Exactly f our interior angles of a hexagon are congruent. The other two interior

angles are complementary. What is the measure of one of the f our congruent

angles?

ERROR ANALYSIS4. ERROR ANALYSIS: Meg A. Byte claimed that she measured an angle of a regular

polygon to be 130◦. Explain why this result is impossible. Use complete sentences, and

examples, if necessary. Spaces have been provided f or each.

_______________________________________ _______________________________________ _______________________________________ _______________________________________

Example:

ALGEBRA

1. Given the f ollowing diagram, find x, then find the measure of the missing angles.

X = _______ m ∠ T = _______ m ∠ TUS = _______ m ∠ TUA = _______

6. PACKAGING. A nut container has the shape of a regular hexagon. I t fi ts in a triangular gif t box. Two cheese wedges fi ll each corner of the box. Find the measure of each angle of one cheese wedge. Show ALL work.

More Applications

ALGEBRA: The car at each vertex of a Ferris wheel holds a maximum of 5 people. The sum of the measures of the interior angles of the Ferris wheel is 7, 740. What is the maximum number of people that the Ferris wheel can hold?

 

Exactly four interior angles of a hexagon are congruent. The other two interior angles are supplementary. What is the measure of one of the four congruent angles?

Triangle Inequalities

Determine whether it is possible to draw a triangle with sides of the given measures. If possible, write yes. If not possible, write no. Be prepared to explain your reasoning.

1.) 3cm, 4 cm, 5cm 2.) 4 m, 5m, 9m

In problems 3, the letter on each side of the ∆s indicates the size of that side. In problems 4, the letter indicates the size of the angle. Rank order the letters from large to small. NOTE: You may need to use ∆ Sum to determine missing angle measures in some triangles3. 4.

Triangle Inequalities

Two side lengths of a triangle are given. Write an inequality to show the range of values for x, the length of the third side.

4 in. , 7in

Isosceles Triangles Practice

Draw an isosceles triangle where one angle measures 58 degrees,  and another angle measures 61 degrees.  Fill in the measurements of all three angles and indicate which sides are congruent.

Applications: Isosceles Triangles Practice

Isosceles Triangles Practice Using Algebra