△DPZ can be mapped onto triangle, W, V, C△WVC by a reflection. If m, angle, P, equals, 39, degreesm∠P=39

Question

∘
and m, angle, D, equals, 113, degreesm∠D=113
∘
, find m, angle, Cm∠C.
Answer
Attempt 1 out of 2

m, angle, Cm∠C
be determined.

Answer 1

To find \( m \angle C \) in triangle \( DPZ \), we use the property of the angles in a triangle, which states that the sum of the interior angles in any triangle is \( 180^\circ \).

We are given:

• \( m \angle P = 39^\circ \)
• \( m \angle D = 113^\circ \)

Let's denote \( m \angle C \) as \( x \).

The equation for the sum of the angles in triangle \( DPZ \) can be set up as:

\[ m \angle P + m \angle D + m \angle C = 180^\circ \]

Substituting the known values into the equation:

\[ 39^\circ + 113^\circ + x = 180^\circ \]

Now, add \( 39 \) and \( 113 \):

\[ 152^\circ + x = 180^\circ \]

Next, we can find \( x \) by isolating it:

\[ x = 180^\circ - 152^\circ \]

\[ x = 28^\circ \]

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

\[ \boxed{28^\circ} \]