Respuesta :

Answer: To find the value of x, we can use the fact that the sum of supplementary angles is 180 degrees.

So, we have:

∠ABC + ∠CBD = 180

Substitute the given angle measures:

(3x + 25) + 32 = 180

Simplify the equation:

3x + 57 = 180

Now, solve for x:

3x = 180 - 57 3x = 123 x = 123 / 3 x = 41

Therefore, the equation to solve for x is:

3x + 57 = 180 3(41) + 57 = 180 123 + 57 = 180 180 = 180

So, x = 41.

Step-by-step explanation: thx

msm555

Answer:

Equation: [tex]\sf (3x + 25) + 32 = 180[/tex]

[tex]\sf x = 41 [/tex]

Step-by-step explanation:

Two angles are supplementary when their measures add up to 180 degrees. Thus, the equation to solve for [tex]\sf x [/tex] is:

[tex]\sf \angle ABC + \angle CBD = 180^\circ [/tex]

Given that [tex]\sf \angle ABC = (3x + 25)^\circ [/tex] and [tex]\sf \angle CBD = 32^\circ [/tex], substitute these values into the equation:

[tex]\sf (3x + 25)^\circ + 32^\circ = 180^\circ [/tex]

So, the equation to solve for x is:

[tex]\sf (3x + 25) + 32 = 180[/tex]

Let's solve for x.

Combine like terms:

[tex]\sf 3x + 25 + 32 = 180 [/tex]

[tex]\sf 3x + 57 = 180 [/tex]

Now, subtract 57 from both sides:

[tex]\sf 3x = 180 - 57 [/tex]

[tex]\sf 3x = 123 [/tex]

Divide both sides by 3:

[tex]\sf x = \dfrac{123}{3} [/tex]

[tex]\sf x = 41 [/tex]

So, the equation to solve for [tex]\sf x [/tex] is [tex]\sf 3x + 57 = 180 [/tex], and the value of [tex]\sf x [/tex] is 41.

To find the measures of [tex]\sf \angle ABC [/tex] and [tex]\sf \angle CBD [/tex]:

[tex]\sf \angle ABC = (3 \times 41 + 25)^\circ = 123 + 25 = 148^\circ [/tex]

[tex]\sf \angle CBD = 32^\circ [/tex]

Therefore, [tex]\sf \angle ABC = 148^\circ [/tex] and [tex]\sf \angle CBD = 32^\circ [/tex].

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