Question

Graph ABCD with B(0, 6). C(2. -5). D(-8, -1), then order the angle measures from least to greatest.

Answer 1

the measure of the angle from least to greatest

Step-by-step explanation:

B(0, 6)

C(2. -5)

D(-8, -1)

Plotting the points on a graph:

To determine the angles from the least to the greatest, we need to find the distance between the points.

distance formula:

`dis\tan ce\text{ = }\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}`
`\begin{gathered} \text{Distance BC = }\sqrt[]{(-5_{}-6)^2+(2_{}-0)^2} \\ =\text{ }\sqrt[]{(-11)^2+(2)^2}\text{ = }\sqrt[]{121\text{ + 4}}\text{ = }\sqrt[]{125\text{ }} \\ \text{Distance BC = 1}1.18 \end{gathered}`
`\begin{gathered} x_1=2,y_1=-5,x_2=-8,y_2\text{ = -1} \\ \text{Distance CD = }\sqrt[]{(-1-(_{}-5))^2+(-8_{}-2)^2} \\ \text{Distance CD = }\sqrt[]{(-1+5)^2+\mleft(-10\mright)^2} \\ =\text{ }\sqrt[]{(4)^2+100}\text{ = }\sqrt[]{116} \\ \text{Distance CD = 10.77} \end{gathered}`
`\begin{gathered} x_1=0,y_1=6,x_2=-8,y_2\text{ = -1} \\ \text{Distance BD = }\sqrt[]{(-1-_{}6)^2+(-8_{}-0)^2} \\ =\sqrt[]{(-7)^2+(-8)^2\text{ }}\text{ = }\sqrt[]{49\text{ + 64}}\text{ = }\sqrt[]{113} \\ \text{Distance BD= }10.63 \end{gathered}`

The higher the length, the higher the angle

BC > CD and CD > BD

From the least to the greatest, the distance between the points are:

BD, CD, BC

The angles are opposite the distance and corresponds to each other

Following the arrangement of the distance,

Hence, the measure of the angle from least to greatest