Find m∠SRT given the diagram with angle measures 45x and 46x-1.
Understand the Problem
The question asks to find the measure of angle SRT, given a geometric figure with angle expressions involving 'x'. Since sides QR = QT and ST = RS, then angle QRT = angle QTR, and angle STR = angle TSR. Also RT is shared, therefore triangles QRT and SRT are isosceles triangles. We can set up an equation where 45x = 46x - 1 and solve for X, then plug in the value to find the size of the required angle.
Answer
$m\angle SRT = 45^\circ$
Answer for screen readers
$m\angle SRT = 45^\circ$
Steps to Solve
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Identify the relationship between the angles
Since ST = RS, triangle SRT is isosceles. Therefore, $\angle SRT = \angle STR$. Given $\angle STR = 45x$ and $\angle SRT = 46x - 1$, we can set up an equation to solve for $x$.
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Solve for x
Equate the two angle expressions:
$45x = 46x - 1$
Subtract $46x$ from both sides:
$-x = -1$
Multiply both sides by $-1$:
$x = 1$
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Find the measure of angle SRT Now that we have the value of $x$, substitute it into the expression for $\angle SRT$:
$\angle SRT = 46x - 1 = 46(1) - 1$
$\angle SRT = 46 - 1 = 45$
$m\angle SRT = 45^\circ$
More Information
The measure of angle SRT is 45 degrees. Notice that angle STR is also 45 degrees. This makes triangle SRT an isosceles triangle as expected.
Tips
A common mistake would be to incorrectly set up the equation or make an error in solving for $x$. It's crucial to correctly equate the two angle expressions based on the properties of the isosceles triangle. Also, plugging in the value of $x$ into the wrong expression, for example angle QRT instead of angle SRT.
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