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One interior angle of a triangle is [tex]45^{\circ}[/tex], and the other two angles are congruent. Choose the equation that could be used to determine the degree measure of one of the congruent angles.

A. [tex]x + 45 = 180[/tex]

B. [tex]x - 45 = 90[/tex]

C. [tex]2x + 45 = 180[/tex]

D. [tex]2x - 45 = 90[/tex]

Sagot :

GinnyAnsweridn
To determine the degree measure of one of the congruent angles in the given triangle, let's follow the step-by-step reasoning.

We know that:

1. The sum of the interior angles in any triangle is [tex]\(180^\circ\)[/tex].
2. One of the angles in the triangle is [tex]\(45^\circ\)[/tex].
3. The other two angles are congruent, meaning they are equal.

Let's denote the measure of one of the congruent angles by [tex]\(x\)[/tex]. Since the two angles are congruent, both of them are equal to [tex]\(x\)[/tex].

Using these facts, we can set up the following equation for the sum of the interior angles of the triangle:

[tex]\[ x + x + 45^\circ = 180^\circ \][/tex]

Combine the terms involving [tex]\(x\)[/tex]:

[tex]\[ 2x + 45^\circ = 180^\circ \][/tex]

So, we have:

[tex]\[ 2x + 45 = 180 \][/tex]

This is the equation that represents the sum of the interior angles of the triangle and can be used to determine the degree measure of one of the congruent angles.

Therefore, the correct equation is:

[tex]\[ 2x + 45 = 180 \][/tex]
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