The \( m \angle D \) is supplementary to the \( m \angle E \). The \( m \angle F \) is supplementary to the \( m \angle E \). If \( m \angle F=113^{\circ} \), what is the \( m \angle D \) and the \( m \angle E \) ?
Upstudy AI Solution
Answer
Solution

Sign in to Unlock Answers for Free!
A Learning Platform Trusted by Millions of Real Students and Teachers.

Answered by UpStudy AI and reviewed by a Professional Tutor
The Deep Dive
Since \( m \angle F \) is supplementary to \( m \angle E \), we know that: \[ m \angle F + m \angle E = 180^\circ \] Substituting \( m \angle F = 113^\circ \): \[ 113^\circ + m \angle E = 180^\circ \] To find \( m \angle E \), we subtract \( 113^\circ \) from \( 180^\circ \): \[ m \angle E = 180^\circ - 113^\circ = 67^\circ \] Now, since \( m \angle D \) is also supplementary to \( m \angle E \): \[ m \angle D + m \angle E = 180^\circ \] Substituting \( m \angle E = 67^\circ \): \[ m \angle D + 67^\circ = 180^\circ \] To find \( m \angle D \), we subtract \( 67^\circ \) from \( 180^\circ \): \[ m \angle D = 180^\circ - 67^\circ = 113^\circ \] So, \( m \angle D = 113^\circ \) and \( m \angle E = 67^\circ \).