Question

1. x=__ find the value of x 11. ∠2=__ find the measure of ∠2. m∠2=x + 94

Explanation:

Step1: Identify the triangle type for problem 10

The triangles in problem 10 are equilateral. In an equilateral triangle, each angle is \(60^{\circ}\). The sum of angles around a point is \(360^{\circ}\). So, \(x = 360-(60 + 60+60)\).

Step2: Calculate \(x\) for problem 10

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Step3: Use the property of congruent triangles for problem 11

The two triangles in problem 11 are congruent (by SSS - Side - Side - Side congruence as the sides are marked equal). So, \(\angle2\) is twice the \(47^{\circ}\) angle (using the exterior angle property or angle - sum relation in congruent triangles). Let's first find \(x\). Since the triangles are congruent, \(x = 47\). Then \(m\angle2=x + 94\).

Step4: Calculate \(m\angle2\) for problem 11

Substitute \(x = 47\) into \(m\angle2=x + 94\).

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Answer:

1. \(120\)
2. \(141\)