What is the value of x? Identify the missing justifications.
measure of angle P Q R equals x plus 7, measure of angle S Q R equals x plus 3, and measure of angle P Q R plus measure of angle S Q R equals measure of angle P Q S equals 100
Three rays originate from a common point Q at the lower left. Ray Q S extends to the right. Ray Q R extends up and to the right. Ray Q P extends up and slightly left.
measure of angle P Q R plus measure of angle S Q R equals measure of angle P Q S a. ______
x + 7 + x + 3 = 100 b. Substitution Property
2x + 10 = 100 c. Simplify
2x = 90 d. ______
x = 45 e. Division Property of Equality
(1 point)
Responses
Angle Addition Postulate; Addition Property of Equality
Angle Addition Postulate; Addition Property of Equality
Angle Addition Postulate; Subtraction Property of Equality
Angle Addition Postulate; Subtraction Property of Equality
Protractor Postulate; Addition Property of Equality
Protractor Postulate; Addition Property of Equality
Protractor Postulate; Subtraction Property of Equality
Angle Addition Postulate; Subtraction Property of Equality
Name the Property of Equality that justifies this statement:
If p = q then p + s = q + s.
(1 point)
Responses
Reflexive Property
Reflexive Property
Multiplication Property
Multiplication Property
Symmetric Property
Symmetric Property
Addition Property
Addition Property
Use the given property to complete the statement.
Multiplication Property of Equality
If 6x ÷ 8 = 40, then ______ .
(1 point)
Responses
6x · 8 = 320
6 x · 8 = 320
40 = 6x · 8
40 = 6 x · 8
6x = 320
6 x = 320
40 = 6x ÷ 8
6x · 8 = 320
Name the Property of Congruence that justifies the statement:
If modifying above upper X upper Y with bar approximately equal to symbol modifying above upper W upper X with bar then modifying above upper W upper X with bar approximately equal to symbolmodifying above upper X upper Y with bar.
(1 point)
Responses
Symmetric Property
Symmetric Property
Transitive Property
Transitive Property
Reflexive Property
Reflexive Property
none of the above
To find the value of x, we can use the given information and follow these steps:
1. From the given information, we know that the measure of angle PQR is equal to x + 7, the measure of angle SQR is equal to x + 3, and the measure of angle PQS is equal to 100.
2. According to the Angle Addition Postulate, the sum of the measures of angles PQR and SQR should be equal to the measure of angle PQS.
3. So we can write the equation: (x + 7) + (x + 3) = 100.
4. To solve this equation, we can apply the Substitution Property, which allows us to substitute the given values for angle measures.
5. Simplifying the equation, we get 2x + 10 = 100.
6. We can then use the Subtraction Property of Equality to subtract 10 from both sides: 2x = 90.
7. Finally, we can use the Division Property of Equality to divide both sides by 2, resulting in x = 45.
So the value of x is 45. The missing justifications are:
b. Substitution Property (used to substitute the given angle measures into the equation)
d. Subtraction Property of Equality (used to subtract 10 from both sides of the equation)
e. Division Property of Equality (used to divide both sides by 2)