"Write a set of inequalities and solve to find the range of possibilities for x. You will need to write two separate inequalities instead of one compound inequality."

Step-by-step explanation:

First, the side lengths should be greater than zero:

Second, The triangles have a common side and the given sides are opposite of 27° and 37° angles.

This tells us the side opposite of greater angle is greater:

Simplify each inequality:

Common solution is:

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.