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

What is the measure of ∠X?

Netzer7
Jun 6, 2017

#1**0 **

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

Guest Jun 6, 2017

#2**+1 **

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