In the figure, angles BCE and CED are equal due to the angle bisector theorem. In the isosceles right-angled triangle BCD, the value of s is determined to be 6 from the provided angle measurements.
In the provided figure, from point C, three lines CD, CB, and CE are drawn. Angle BCE is labeled as 7s, and angle DCE is expressed as s + 36. It is stated that CE bisects angle C, and BE = ED = 52.
Now, focusing on triangle BCE, due to the angle bisector theorem, angles BCE and CED are equal since BE = ED.
Moving on to triangle BCD, angles B and D are both right angles (90 degrees), and BE = ED. Thus, triangle BCD is an isosceles right-angled triangle.
In such triangles, the angles opposite the equal sides are equal. Therefore, angles BCE and CED are equal.
Setting up an equation based on the given information:
7s = s + 36
Solving for s:
6s = 36
s = 6
Hence, the value of s is 6.