Mathematics
Grade 4
15 min
Solve a system of equations using elimination: word problem
Solve a system of equations using elimination: word problem
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Introduction & Learning Objectives
Learning Objectives
Identify two different clues about two mystery angles in a word problem.
Write two 'angle sentences' that represent the clues.
Use the 'finding the difference' (elimination) method to solve for one mystery angle.
Substitute the value of the first angle to find the value of the second angle.
Check their answers using both original clues.
Define complementary and supplementary angles in the context of a word problem.
Solve simple angle-based word problems that require finding two unknown values.
Can you solve a mystery with two secret clues? 🕵️♀️ Let's become angle detectives and find the size of two mystery angles!
In this lesson, we will learn a special trick called 'elimination' to solve angle puzzles. It's lik...
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Key Concepts & Vocabulary
TermDefinitionExample
Mystery AngleAn angle whose size (in degrees) we don't know yet. We use clues to figure it out.In a puzzle, we might have a 'big mystery angle' and a 'small mystery angle'.
Angle SentenceA sentence that describes a clue about how mystery angles are related. It's like an equation, but in words and pictures.Clue 1: One big angle + one small angle = 90°.
System of EquationsA set of two or more 'angle sentences' or clues that we use together to solve a puzzle with two or more mystery angles.Clue 1: Big Angle + Small Angle = 90°. Clue 2: Big Angle + Big Angle + Small Angle = 130°. We need both clues to solve it.
Elimination (Finding the Difference)A method where we find the difference between two angle sentences to get rid of one of...
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Core Formulas
The Angle Sentence Rule
(Combination of Angles 1) = Total_1
(Combination of Angles 2) = Total_2
Every word problem gives you two clues. Your first job is to turn each clue into an 'Angle Sentence'. This helps you see the puzzle clearly.
The Elimination Rule (Finding the Difference)
(Sentence 2) - (Sentence 1) = (Difference in Angles) = (Difference in Totals)
Subtract the smaller angle sentence from the larger one. This 'eliminates' the parts that are the same, leaving you with a simple clue to find the first mystery angle.
4 more steps in this tutorial
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Challenging
Angle A and two of Angle B add up to 180°. Angle A and one of Angle B add up to 110°. What is the size of Angle B?
A.110°
B.70°
C.40°
D.180°
Challenging
The sum of a big angle and a small angle is 120°. The sum of the big angle and three small angles is 180°. What is the size of the big angle?
A.90°
B.30°
C.60°
D.120°
Challenging
A diagram shows a straight line. On the line, there is one big angle (B) and two identical small angles (S), and together they make 180°. A separate clue says that one big angle (B) and one small angle (S) add up to 135°. What is the size of the big angle?
A.45°
B.180°
C.90°
D.135°
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