\A and \B are supplementary angles. If m\A= (3x – 23) and m \B = (2x – 12), then find the measure of \B.

2 supplementary angles when added together need to equal 180 degrees.

Add:

3x-23 + 2x-12 = 180

Simplify:

5x -35 = 180

Add 35 to both sides:

5x = 215

Divide both sides by 5:

X = 43

Now replace x with 43 in the equation for angle b:

2(43) -12 = 86-12 = 74 degrees

Angle B = 74 degrees

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'.