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Solve for x Using Perpendicular Square Diagonals Property
Mathematics
Grade 8 (Junior High School)
Question Content
In square PQSR with diagonals intersecting at T, the measure of ∠PTQ is (6x - 21)°. Solve for x.
Correct Answer
x = 18.5
Detailed Solution Steps
1
Step 1: Recall that the diagonals of a square are perpendicular, so the angle formed at their intersection ∠PTQ = 90°.
2
Step 2: Set up the equation: \(6x - 21 = 90\).
3
Step 3: Solve for x: Add 21 to both sides: \(6x = 111\). Divide both sides by 6: \(x = 18.5\).
Knowledge Points Involved
1
Perpendicular Diagonals of a Square
The diagonals of a square intersect at a 90° angle, which is a key property used to set up equations for variable problems.
2
Solving Linear Equations
Linear equations of the form \(ax + b = c\) are solved by isolating the variable using inverse operations (addition/subtraction first, then multiplication/division).
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