Question

1. $mangle2 = 6x + 3$
2. $mangle2=x + 49$

Explanation:

1. For problem 9:

• Explanation:
• Step1: Recall the property of an isosceles - right triangle
• In the first right - triangle, since the two legs are congruent, the non - right angles are equal. The sum of the interior angles of a triangle is \(180^{\circ}\), and in a right - triangle with two equal non - right angles, each non - right angle is \(45^{\circ}\). So we set up the equation \(6x + 3=45\).
• Step2: Solve the equation for \(x\)
• Subtract 3 from both sides of the equation \(6x+3 = 45\): \(6x=45 - 3\), so \(6x = 42\).
• Then divide both sides by 6: \(x=\frac{42}{6}=7\).
• Answer: A. 7

1. For problem 10:

• Explanation:
• Step1: Recall the property of an isosceles triangle
• In the second isosceles triangle, the two base angles are equal. The sum of the interior angles of a triangle is \(180^{\circ}\). Let the base angles be equal. One base angle is \(42^{\circ}\), and the other is \(m\angle2=x + 49\). So \(x+49 = 42\).
• Step2: Solve the equation for \(x\)
• Subtract 49 from both sides of the equation \(x + 49=42\): \(x=42-49=-7\).
• Answer: D. - 7

Answer:

1. For problem 9:

• Explanation:
• Step1: Recall the property of an isosceles - right triangle
• In the first right - triangle, since the two legs are congruent, the non - right angles are equal. The sum of the interior angles of a triangle is \(180^{\circ}\), and in a right - triangle with two equal non - right angles, each non - right angle is \(45^{\circ}\). So we set up the equation \(6x + 3=45\).
• Step2: Solve the equation for \(x\)
• Subtract 3 from both sides of the equation \(6x+3 = 45\): \(6x=45 - 3\), so \(6x = 42\).
• Then divide both sides by 6: \(x=\frac{42}{6}=7\).
• Answer: A. 7

1. For problem 10:

• Explanation:
• Step1: Recall the property of an isosceles triangle
• In the second isosceles triangle, the two base angles are equal. The sum of the interior angles of a triangle is \(180^{\circ}\). Let the base angles be equal. One base angle is \(42^{\circ}\), and the other is \(m\angle2=x + 49\). So \(x+49 = 42\).
• Step2: Solve the equation for \(x\)
• Subtract 49 from both sides of the equation \(x + 49=42\): \(x=42-49=-7\).
• Answer: D. - 7