Question

Find m∠ABD and m∠CBD given m∠ABC = 111∘
The Equations are (-10x+58)∘ and (6x+41∘)
Write and Solve an equation

Answer 1

Answer:

x=-3

<ABD=88

<CBD=23

Step-by-step explanation:

We know that <ABC is made up of 2 angles: <ABD and <CBD.

We also know that the m<ABC is 111.

Therefore, <ABD and <CBD added together must equal 111.

<ABD+ <CBD =111

We know that <ABD is -10x+58 and <CBD is 6x+41, so we can substitute these in.

-10x+58+6x+41=111

Combine like terms

(-10x+6x)+(58+41)=111

-4x+99=111

Now we need to solve for x. First, move all the constants to the same side. Subtract 99 from both sides, since 99 is being added to -4x.

-4x+99-99=111-99

-4x=12

Next, divide both sides by -4, since -4 and x are being multiplied.

-4x/-4=12/-4

x=-3

Now we know x, and can substitute it in to find the angle measures.

<ABD

-10x+58

-10(-3)+58

30+58

88

<CBD

6x+41

6(-3)+41

-18+41

23

Answer 2

$m \angle ABD = 88^{\circ}\\m \angle CBD = 23^{\circ}$

Given:

m∠ABC = 111∘

m∠ABD = (-10x+58)∘

m∠CBD = (6x+41)∘

First, find the value of x by creating an equation

Thus:

$m\angle ABD + m \angle CBD = m \angle ABC$ (angle addition postulate)

Substitute

$(-10x+58) + (6x+41) = 111$

Solve for x

$-10x+58 + 6x+41 = 111$]

Add like terms

$-10x+58 + 6x+41 = 111\\-4x + 99 = 111\\-4x = 111 - 99\\-4x = 12$

Divide both sides by -4

$x = -3$

Find m∠ABD and m∠CBD by plugging in the value of x

$m\angle ABD = -10x + 58 \\m\angle ABD = -10(-3) + 58 \\m\angle ABD = 88^{\circ}$

$m \angle CBD = 6x + 41\\m \angle CBD = 6(-3) + 41\\m \angle CBD = 23^{\circ}$

Therefore:

$m \angle ABD = 88^{\circ}\\m \angle CBD = 23^{\circ}$

Learn more here:

https://brainly.com/question/4208193