To solve this problem, we can use the information provided about the angles to set up an equation.
We know that:
- \( m \angle B = 58^\circ \)
- The sum of \( m \angle E \) and \( m \angle D \) is \( 122^\circ \).
From this, we can express the relationship as:
\[ m \angle E + m \angle D = 122^\circ \]
If we assume \( m \angle E \) is the remaining degrees needed to make a complete system with angle B, or you could just simply isolate one angle.
1. Setting up the equation:
Let's solve for \( m \angle D \):
\[ m \angle E = 122^\circ - m \angle D \]
2. Finding angle D:
Assuming, for instance, that \( \angle B, \angle E, \) and \( \angle D \) are part of a larger angle configuration where assuming a rule that states certain relationships like maybe some of them are supplementary or adjacent angles, you'd want to provide the relationship as needed.
However, given the information, we need more data (like if they're supplementary, or part of a triangle).
If it's supplementary to angle B:
\[ m \angle E + m \angle D = 180^\circ - m \angle B \]
Replace \( m \angle B \) with 58:
\[ m \angle E + m \angle D = 180^\circ - 58^\circ \ m \angle E + m \angle D = 122^\circ \]
So, actually, we can directly solve:
Assuming if \( D\) takes the minimum value: Let’s say we take \(m \angle D\) as \(x\):
\[ m \angle E = 122^\circ - x \]
The simplest case to calculate the values under assumption:
To simplify:
If we find that the same relationship holds we can directly see this similar condition holds true by solving out clothing degrees:
Say \(m \angle D\) as \(x\):
\[ x + 58 = 122 \] \[ x = 122 - 58 \]
Therefore:
\[ m \angle D = 64^\circ \]
Answer:
Equation to use: \( m \angle E + m \angle D = 122^\circ \)
Value of \( m \angle D \): \( 64^\circ \)
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