\( \triangle A B C \cong \triangle D E F \). Find the measure of the given angles. \( m \angle A=x+25 \) \( m \angle D=2 x \) \( \begin{array}{l}m \angle A=\square^{\circ} \\ \text { (Do not include the degree symbol in your answer.) } \\ m \angle D=\square^{\circ} \\ \text { (Do not include the degree symbol in your answer.) }\end{array} \)
Solución de inteligencia artificial de Upstudy
Responder
Solución

¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

Respondido por UpStudy AI y revisado por un tutor profesional
Mind Expander
Since the triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent, their corresponding angles are equal. Therefore, we can set up the equation: \[ x + 25 = 2x \] To solve for \( x \), we subtract \( x \) from both sides: \[ 25 = 2x - x \] \[ 25 = x \] Now we can find the measures of the angles: For \( m \angle A \): \[ m \angle A = x + 25 = 25 + 25 = 50 \] For \( m \angle D \): \[ m \angle D = 2x = 2 \times 25 = 50 \] Thus, the measures of the angles are: \( m \angle A = 50 \) \( m \angle D = 50 \) The final answers are: \[ \begin{array}{l} m \angle A = 50 \\ m \angle D = 50 \end{array} \]
