Finding the measure of angle 1
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What is the measure of angle 1?
This question includes visual content: The image shows a geometric diagram featuring two triangles. On the left is an isosceles triangle with an apex angle of 48 degrees, indicated by marks on the two sides meeting at that apex. Below this isosceles triangle, there is a triangle formed by angles 1, 2, and 3. On the right, there is a right-angled triangle (indicated by a square symbol) with one internal angle of 65 degrees. All these shapes are interconnected by a common horizontal line segment.
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In this problem, we need to find the measure of angle one by analyzing the geometric relationships between the three connected triangles.
Finding Angle Measure
Let's start with the triangle on the far left. Notice the two tick marks on the sides, which indicate that this is an isosceles triangle.
The top angle is forty-eight degrees. Since the base angles of an isosceles triangle are equal, let's call each base angle 'x' and solve for it.
Combining the like terms, we get two x plus forty-eight equals one hundred and eighty.
Subtracting forty-eight from both sides, we find that two x equals one hundred and thirty-two.
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