Geometry Problem Set - Angles and Equations

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Questions and Answers

What is the value of x in the equation 16x - 8 = 120?

4
10
8 (correct)
6

In the equation m∠QXR = (3x + 3)° and m∠RXS = (4x + 6)°, what would be the next step after setting up 2(4x + 6) = 3x + 3?

Moving all terms involving *x* to one side
Setting the expression to equal 0
Distributing to get 8*x* + 12 (correct)
Combining like terms to get 2*x* + 3

What is the sum of the angles m∠RZS and m∠SZT if m∠RZS is expressed as (6x - 13)° and m∠SZT as (10x + 5)°?

10*x* + 8
16*x* - 8 (correct)
10*x* - 8
16*x* + 8

If 3x - 63 = x + 37, what operation would you perform first to isolate x?

Subtract x from both sides (C) Signup and view all the answers

What is the possible outcome for x if 5x = -9?

-1.8 (A) Signup and view all the answers

Flashcards

Angle Addition Postulate

The measure of an angle is the sum of the measures of its non-overlapping parts.

Angle Bisector

A bisector divides an angle or segment into two congruent parts.

Triangle Angle Sum Theorem

The sum of the measures of the angles in a triangle is 180°.

Solving for a Variable

To solve for a variable, use inverse operations and isolate the variable on one side of the equation.

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Angle Bisector Theorem

If a line (or ray or segment) bisects an angle, then the measure of each of the resulting angles is half the measure of the original angle.

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Study Notes

Problem 15

Find x if m∠RZT = 120°, m∠RZS = 6x - 13°, and m∠SZT = 10x + 5°
The angles RZS and SZT form a larger angle, RZT. This means (6x - 13) + (10x + 5) = 120
Solve for x: 16x - 8 = 120; 16x = 128; x = 8

Problem 16

XS bisects ∠RXT. m∠QXR = (3x + 3)° and m∠RXS = (4x + 6)°
An angle bisector divides an angle into two equal parts. So m∠RXS = m∠TXS
4x + 6 = 3x + 3
Solve for x: x= -3
If x = -3, it is not possible to solve.

Problem 17

Find the value of x, given that 3x - 63 = x + 37
Solve for x, 2x = 100; x = 50

Problem 18

Find x in the figure
The angles form a right angle (90°)
4x + 60 + 90 - 4x = 180 (solve) - this problem is problematic as it is unclear which angles are in question.

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Description

This quiz consists of various geometry problems involving angles and algebraic equations. Participants will solve for the variable x in different angle configurations and equations. Test your understanding of angle relationships and algebraic manipulation with these problems.