Question

1. find ∠4 if △xyz is not regular but ∠1 = 40° and m∠2 = 35°.

Explanation:

1. Explanation:

• Step1: Recall the angle - sum property of a triangle
• The sum of the interior angles of a triangle is \(180^{\circ}\). In \(\triangle XYZ\), if we assume that \(\angle1\), \(\angle2\), and \(\angle4\) are the interior angles of the triangle.
• Step2: Set up the equation
• According to the angle - sum property of a triangle, \(\angle1+\angle2+\angle4 = 180^{\circ}\).
• We know that \(\angle1 = 40^{\circ}\) and \(\angle2=35^{\circ}\). Substitute these values into the equation: \(40^{\circ}+35^{\circ}+\angle4 = 180^{\circ}\).
• First, add the known angles on the left - hand side: \(40^{\circ}+35^{\circ}=75^{\circ}\). So the equation becomes \(75^{\circ}+\angle4 = 180^{\circ}\).
• Step3: Solve for \(\angle4\)
• Subtract \(75^{\circ}\) from both sides of the equation: \(\angle4=180^{\circ}-75^{\circ}\).
• \(\angle4 = 105^{\circ}\).

1. Answer:

\(105^{\circ}\)

Answer:

1. Explanation:

• Step1: Recall the angle - sum property of a triangle
• The sum of the interior angles of a triangle is \(180^{\circ}\). In \(\triangle XYZ\), if we assume that \(\angle1\), \(\angle2\), and \(\angle4\) are the interior angles of the triangle.
• Step2: Set up the equation
• According to the angle - sum property of a triangle, \(\angle1+\angle2+\angle4 = 180^{\circ}\).
• We know that \(\angle1 = 40^{\circ}\) and \(\angle2=35^{\circ}\). Substitute these values into the equation: \(40^{\circ}+35^{\circ}+\angle4 = 180^{\circ}\).
• First, add the known angles on the left - hand side: \(40^{\circ}+35^{\circ}=75^{\circ}\). So the equation becomes \(75^{\circ}+\angle4 = 180^{\circ}\).
• Step3: Solve for \(\angle4\)
• Subtract \(75^{\circ}\) from both sides of the equation: \(\angle4=180^{\circ}-75^{\circ}\).
• \(\angle4 = 105^{\circ}\).

1. Answer:

\(105^{\circ}\)