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By the [tex]\(\square\)[/tex], the sum of the angles in a triangle is equal to [tex]\(180^{\circ}\)[/tex]. Therefore, [tex]\(m \angle A + m \angle B + m \angle C = 180^{\circ}\)[/tex].

Using the [tex]\(\square\)[/tex] 180. Using the [tex]\(\square\)[/tex] [tex]\(7x = 84\)[/tex]. Then, using the division property of equality, [tex]\(x = 12\)[/tex].

To find the measure of angle [tex]\(A\)[/tex], use the substitution property to get [tex]\(m \angle A = 6(12)^{\circ}\)[/tex]. Finally, simplifying the expression gives [tex]\(m \angle A = 72^{\circ}\)[/tex].



Answer :

GinnyAnswer
Certainly! Let's go through the problem step by step.

1. Sum of Angles in a Triangle:
It's a fundamental property of triangles that the sum of their interior angles is always [tex]\( 180^\circ \)[/tex]. We can express this as:
[tex]\[ m \angle A + m \angle B + m \angle C = 180^\circ \][/tex]

2. Given Equation:
We are given an equation related to one of the angles in the triangle:
[tex]\[ 7x = 84 \][/tex]

3. Solving for [tex]\( x \)[/tex]:
To find [tex]\( x \)[/tex], we use the division property of equality. We divide both sides of the equation by 7:
[tex]\[ x = \frac{84}{7} \][/tex]
Simplifying this gives:
[tex]\[ x = 12 \][/tex]

4. Finding the Measure of Angle [tex]\( A \)[/tex]:
We are told to use the substitution property to find the measure of angle [tex]\( A \)[/tex]. According to the problem, we need to calculate:
[tex]\[ m \angle A = 6x \][/tex]
Substituting [tex]\( x = 12 \)[/tex] into the expression:
[tex]\[ m \angle A = 6 \times 12 \][/tex]
Simplifying this gives:
[tex]\[ m \angle A = 72^\circ \][/tex]

So, by following these steps, we find that the measure of angle [tex]\( A \)[/tex] is [tex]\( 72^\circ \)[/tex], and the sum of the angles in the triangle is indeed [tex]\( 180^\circ \)[/tex].

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