Drag and drop the measurement to identify the m∠D

Question

.
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ΔDEF
is similar to ΔXYZ
. ΔDEF
has angles D, E, and F, with m∠E=45
and m∠F=25
. What is m∠X
?

The \(m\angle X=\)Response area for the measure of angle D..

Answer 1

To find \(m\angle D\), we first need to consider the fact that the sum of the angles in any triangle is always 180 degrees.

In triangle \( \Delta DEF \):

\[ m\angle D + m\angle E + m\angle F = 180^\circ \]

Given \( m\angle E = 45^\circ \) and \( m\angle F = 25^\circ \):

\[ m\angle D + 45^\circ + 25^\circ = 180^\circ \]

Combining the known angles:

\[ m\angle D + 70^\circ = 180^\circ \]

Now, we subtract 70 degrees from both sides:

\[ m\angle D = 180^\circ - 70^\circ = 110^\circ \]

Since triangles \( \Delta DEF \) and \( \Delta XYZ \) are similar, their corresponding angles are equal. Therefore, \( m\angle X \) corresponds to \( m\angle D \):

\[ m\angle X = m\angle D = 110^\circ \]

Thus, the measure of angle \( \angle X \) is:

\[ m\angle X = 110^\circ \]

So the final response for the measure of angle \( \angle D \) is 110.