Question

triangles finding an angle measure for a triangle sharing a side with another... find the value of x. if necessary, you may learn what the markings on a figure indicate. x =

Explanation:

Step1: Find the base - angle of the larger right - triangle

Since the two segments are equal (marked), the base - angles of the larger right - triangle (excluding the right angle) are equal. Let the base - angle be \(y\). Using the angle sum property of a triangle (\(90^{\circ}+y + y=180^{\circ}\)), we know \(y = 29^{\circ}\).

Step2: Find the base - angle of the smaller right - triangle

Let the base - angle of the smaller right - triangle (excluding the right angle) be \(z\). Using the angle sum property of a triangle (\(90^{\circ}+z+z = 180^{\circ}\)), we get \(z=\frac{180 - 90}{2}=45^{\circ}\).

Step3: Calculate \(x\)

We know that \(x=z - 29^{\circ}\). Substituting \(z = 45^{\circ}\), we have \(x=45^{\circ}-29^{\circ}\).

Answer:

\(x = 16\)