May I please have help? It would be very much appreciated. I will give out a crown

1.

A-5, B-10, C-2 = No, the length will not contruct a triangle

2.

A-8, B-2, C-10 = No, the length will not contruct a triangle

3.

A-13, B-15, C-23 = Yes, they can construct a triangle

4.

A-1, B-17, C-3 = No, the length will not contruct a triangle

5.

A-33, B-30, C-21 = Yes, they can construct a triangle

I really don't know how to explain how I got these answers, but the rule is The Triangle Inequality Theorem. It states that the sum of any 2 sides of a triangle must be greater than the measure of the third side. The picture below should hopefully help.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq