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△RST is similar to triangle △XYZ by theAA Similarity Postulate .

 

What is the measure of  ∠X?

Netzer7  Jun 6, 2017
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 #1
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The measure of the letter "X" is 3/17 In or .3 (3/10 cm) in lenth 4/17 In or .4 cm (4/10cm) highth Your welcome

 

 

coolcoolcool 

Guest Jun 6, 2017
 #2
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Statements Reasons
\(\angle RST\cong\angle XYZ\) Corresponding angles in similar triangles are congruent
\(m\angle RST=m\angle XYZ\) Congruent angles have the same measure, by definition.
\(23^{\circ}=m\angle{XYZ}\) Substitution property of equality OR Transitive property of equality.
\(m\angle{XYZ}+m\angle{YZX}+m\angle{ZXY}=180^{\circ}\) Triangle sum therom (The sum of the interior angles of triangle is 180)
\(23^{\circ}+47^{\circ}+m\angle{ZXY}=180^{\circ}\) Substitution property of equality
\(70^{\circ}+m\angle{ZXY}=180^{\circ}\) Simplify
\(m\angle{ZXY}=110^{\circ}\) Subtraction property of equality
   

 

Thus, \(m\angle{X}=110^{\circ}\)

TheXSquaredFactor  Jun 6, 2017

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