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Question 16 (1 point)

[tex]$\angle 1$[/tex] and [tex]$\angle 2$[/tex] form a linear pair and therefore are supplementary angles. If [tex]$m \angle 1 = 6x + 19$[/tex] and [tex]$m \angle 2 = 5x - 4$[/tex], then [tex]$m \angle 1$[/tex] is:

A. [tex]$71^{\circ}$[/tex]

B. [tex]$109^{\circ}$[/tex]

C. [tex]$45^{\circ}$[/tex]

D. [tex]$91^{\circ}$[/tex]

Sagot :

GinnyAnsweridn
To find the measure of [tex]\( \angle 1 \)[/tex], follow the steps below:

1. Understand the relationship between the angles:
Since [tex]\( \angle 1 \)[/tex] and [tex]\( \angle 2 \)[/tex] form a linear pair, they are supplementary angles. This means their measures add up to 180 degrees.

2. Express the given information in terms of equations:
[tex]\[ m \angle 1 = 6x + 19 \][/tex]
[tex]\[ m \angle 2 = 5x - 4 \][/tex]

3. Set up the equation illustrating their supplementary nature:
[tex]\[ (6x + 19) + (5x - 4) = 180 \][/tex]

4. Combine like terms:
[tex]\[ 6x + 19 + 5x - 4 = 180 \][/tex]
[tex]\[ 11x + 15 = 180 \][/tex]

5. Solve for x:
[tex]\[ 11x + 15 = 180 \][/tex]
Subtract 15 from both sides:
[tex]\[ 11x = 165 \][/tex]
Divide by 11:
[tex]\[ x = 15 \][/tex]

6. Find [tex]\( m \angle 1 \)[/tex]:
Substitute [tex]\( x = 15 \)[/tex] back into the expression for [tex]\( m \angle 1 \)[/tex]:
[tex]\[ m \angle 1 = 6x + 19 \][/tex]
[tex]\[ m \angle 1 = 6(15) + 19 \][/tex]
[tex]\[ m \angle 1 = 90 + 19 \][/tex]
[tex]\[ m \angle 1 = 109 \][/tex]

Therefore, the measure of [tex]\( \angle 1 \)[/tex] is [tex]\( 109^\circ \)[/tex].

So, the correct answer is (b) [tex]\( 109^\circ \)[/tex].
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