The measure of angle 1, m∠1, found using the congruency of the angles and the angle sum property of a triangle is 55°
The angle sum property of a triangle specifies that the sum of the interior angles of a triangle is 180°
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The parameters of the question are;
The number of arcs on angles b and q = Single arcs
Therefore, based on the arc markings indicating congruency of the angles, we get;
Angle b is congruent to angle q ∠b ≅ ∠q
Therefore, ∠b = ∠q, by the definition of congruency
The number of arcs on angle a and angle s = Double arcs
Therefore, angle a is congruent to angle s based on the arc markings, which indicates;
∠a ≅ ∠s
∠a = ∠s by the definition of congruency
The label on angle ∠a = 45°
The label on angle ∠b = 80°
∠a = ∠s, therefore, ∠s = 45°, by substitution property
∠b = ∠q, therefore, ∠q = 80° by substitution
∠s + ∠q + ∠1 = 180° Angle sum property of a triangle
45° + 80° + m∠1 = 180°
m∠1 = 180° - (45° + 80°) = 55°
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