+38 △RST is similar to triangle △XYZ by theAA Similarity Postulate .
What is the measure of ∠X?
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
+2441 | 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, \(m\angle{X}=110^{\circ}\)
