To determine the measure of the given angles, let's follow the conditions and steps provided.
1. Condition 1: [tex]\(m \angle 2 + m \angle 2 = 180^\circ\)[/tex]
We know that the measure of both angles [tex]\( \angle 2 \)[/tex] adds up to [tex]\(180^\circ\)[/tex]:
[tex]\[
m \angle 2 + m \angle 2 = 180^\circ
\][/tex]
Simplifying, we find:
[tex]\[
2m \angle 2 = 180^\circ \implies m \angle 2 = \frac{180^\circ}{2} = 90^\circ
\][/tex]
2. Condition 2: [tex]\(m \angle 2 + m \angle 3 = 180^\circ\)[/tex]
Substituting the value of [tex]\( \angle 2 \)[/tex] found above:
[tex]\[
90^\circ + m \angle 3 = 180^\circ
\][/tex]
Solving for [tex]\( \angle 3 \)[/tex]:
[tex]\[
m \angle 3 = 180^\circ - 90^\circ = 90^\circ
\][/tex]
3. Condition 3: [tex]\(m \angle 3 + m \angle 4 = 180^\circ\)[/tex]
Using the value of [tex]\( \angle 3 \)[/tex] from above:
[tex]\[
90^\circ + m \angle 4 = 180^\circ
\][/tex]
Solving for [tex]\( \angle 4 \)[/tex]:
[tex]\[
m \angle 4 = 180^\circ - 90^\circ = 90^\circ
\][/tex]
4. Condition 4: [tex]\(m \angle 5 + m \angle 6 = 180^\circ\)[/tex]
Without additional context or constraints, we assume [tex]\( \angle 5 \)[/tex] and [tex]\( \angle 6 \)[/tex] to be equal due to symmetry or typical problem setups:
[tex]\[
m \angle 5 + m \angle 6 = 180^\circ
\][/tex]
Using the symmetry assumption:
[tex]\[
\angle 5 = 90^\circ \quad \text{and} \quad \angle 6 = 90^\circ
\][/tex]
Given these steps and conditions, the measures of the angles are:
[tex]\[
m \angle 2 = 90^\circ, \quad m \angle 3 = 90^\circ, \quad m \angle 4 = 90^\circ, \quad m \angle 5 = 90^\circ, \quad m \angle 6 = 90^\circ
\][/tex]
