KM bisects ÐJKL, mÐJKM = (2x + 5)°, and mÐMKL = (5x – 10)°. Find mÐJKM.

15 °

Step-by-step explanation:

An angular bisector can divide the angle in to 2 congruent angles.

According to the question, the angular bisector KM divides J K L angle into 2 congruent angles.

So,

< J K M = < M K L

2x + 5  = 5x - 10

Now let us find the value of x.

2x + 5  = 5x - 10

2x + 5 + 10 = 5x

15 = 5x - 2x

15 = 3x

You can divide both sides by 3.

5 = x

According to the question, we are asked to find the < J K M.

So,

< J K M = 2x + 5

            = 2 × 5 + 5

            = 10 + 5

            = 15

Hope this helps :-)

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'.