Find the measure of angle 4
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What is the measure of angle 4?
This question includes visual content: A geometric figure shows two primary triangles. On the left, an isosceles triangle has a vertex angle labeled 48 degrees, and the two legs are marked with matching tick marks. The base of the triangle lies on a horizontal line. The left triangle shares a vertex with the right triangle at the center. The right triangle has a right angle marked at its top vertex. The internal angle adjacent to the right triangle center is labeled 65 degrees. An exterior angle on the right side is labeled 4. Angles 1, 2, and 3 are marked inside the intersection.
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Step by Step Written Solution
In this problem, we need to find the measure of angle four. We'll work through the connected triangles from left to right.
Finding Angle Measures
Let's start with the isosceles triangle on the far left. Notice the two hash marks indicate that two sides are equal in length.
Because it's an isosceles triangle, the base angles are equal. We can find them by subtracting the vertex angle of forty eight degrees from one hundred eighty degrees and then dividing by two.
So, each base angle is sixty six degrees. We'll mark the right base angle as sixty six.
Next, let's look at angle one. It forms a straight line with the base angle of the first triangle. Angles on a straight line sum to one hundred eighty degrees.
Now, let's move to the middle triangle which contains angles one, two, and three. We just found that angle one is one hundred fourteen degrees.
Middle Triangle Analysis
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