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The sum of the measures of angle [tex]\( M \)[/tex] and angle [tex]\( N \)[/tex] is [tex]\( 90^{\circ} \)[/tex].

- The measure of angle [tex]\( M \)[/tex] is [tex]\( 30^{\circ} \)[/tex].
- The measure of angle [tex]\( N \)[/tex] is [tex]\( (7x + 11)^{\circ} \)[/tex].

What is the value of [tex]\( x \)[/tex]?

A. 5
B. 7
C. 50
D. 100

Answer :

Sure! Let's solve the problem step by step:

1. We are given that the sum of the measures of angle [tex]\( M \)[/tex] and angle [tex]\( N \)[/tex] is [tex]\( 90^\circ \)[/tex].

2. The measure of angle [tex]\( M \)[/tex] is given as [tex]\( 30^\circ \)[/tex].

3. The measure of angle [tex]\( N \)[/tex] is expressed as [tex]\( (7x + 11)^\circ \)[/tex].

4. We can set up the equation based on the information:
[tex]\[
\text{Measure of angle } M + \text{Measure of angle } N = 90^\circ
\][/tex]
[tex]\[
30 + (7x + 11) = 90
\][/tex]

5. Simplify the equation:
[tex]\[
30 + 7x + 11 = 90
\][/tex]

6. Combine the constant terms on the left side:
[tex]\[
7x + 41 = 90
\][/tex]

7. Subtract 41 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
7x = 90 - 41
\][/tex]
[tex]\[
7x = 49
\][/tex]

8. Divide both sides by 7 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{49}{7}
\][/tex]
[tex]\[
x = 7
\][/tex]

Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 7 \)[/tex].

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