Question - Finding Measure of Angle B in Triangle ABC
Solution:
The image shows triangle ABC with a line segment from vertex C to a point D on line segment AB. Point D appears to bisect angle ACB into two equal angles, shown by the single arc marks in each of these angles. The length of BC is given as 6.5 units. The task is to find the measure of angle B in degrees, written as m∠B.Since the angle at C is bisected by CD, the two angles at D are equal. This means that triangle BCD and ACD are similar because they both have a right angle (as implied by the square box symbol at angle A) and they share the bisected angle at C.Given that triangles BCD and ACD are similar, they are also right triangles, and the angles at B and A must add up to 90 degrees because in any triangle the angles sum to 180 degrees, and the right angle takes up 90 degrees of that sum.Since the angles at D are equal, this means the angles at B and A are also equal because they are corresponding angles in similar triangles. Each of these angles must therefore be half of 90 degrees because they add up to 90 degrees themselves.m∠B = 90 degrees / 2 = 45 degrees.Therefore, the measure of angle B is 45 degrees.
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