Angle A and angle B form a liner pair. The measure of angle A is ( 2x+7) and the measure of angle B is (x+20), what is the measure of angle A

Step-by-step explanation:
In this problem, we are dealing with 2 (two) angles:
"Angle A" and "Angle B".
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We are told that Angle A and Angle B form a "linear pair" ;
which means that these are supplementary angles;

→ which means that the sum of the measures of these 2 (two) angles equal 180° ;
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Given: m∡A = 2x + 7 ; and m∡B = x + 20 ;
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We are asked to solve for " m∡A "; which is: "(2x + 7)" .

To do so, let us start by solving for the value of "x".

We can start by setting up the equation:
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" (2x+7) + (x + 20) = 180 " ;

→ 2x + 7 + x + 20 = 180 ;
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Combine the "like terms" on the "left-hand side" of this equation:
→ +2x + x = 2x + 1x = +3x ;
→ +7 + 20 = +27 ;

And rewrite the equation:
→ 3x + 27 = 180 ;

Now, subtract "27" from each side of the equation:
→ 3x + 27 − 27 = 180 − 27 ;

to get:
→ 3x = 153 :

Now divide each side of the equation by "3" ;
to isolate "x" on one side of the equation;
& to solve for "x" ;
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→ 3x / 3 = 153 / 3 ;
To get:
x = 51 .

Now: Since we are given:
" m∡A = 2x + 7 " ;

We can plug in our value of "x"—which is "51" ;
and solve for " m∡A " :
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→ measure of angle A [written as: " m∡A "];

= 2x + 7 ;
= 2(51) + 7 ;
= 102 + 7 = 109.
→ " m∡A = 109° " .
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To check our work:
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→ " m∡A + m∡B = 180 " ;

{Note: If " m∡A = 109 " ; from our obtained solution} ;
then: " 109 + m∡B = 180 " ;
then:
→ " m∡B = 180 − 109 = 71 ."
then:

→ " m∡B = (x + 20) = 71 ;
then:
→ " m∡B = (51 +20) =? 71 ?
{Note: We are given: " m∡B = (x + 20) " ;
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→ So, we plug in "51" (our obtained value for "x"; to see if the equation holds true—as part of "checking our answer."
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→ " (51 + 20) =? 71 ? " ; Yes! ;

So: The correct answer is: " m∡A = 51° " .
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Hope this is helpful to you! Best wishes!
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