Answer: The answer is: " m∡R = 20° " .
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Step-by-step explanation:
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Note that ∡R and ∡Q are "supplementary angles".
In these particular case:
" m∠R + m∠Q = 180 " ;
We are given (in the picture):
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" m∠R = (x - 15) " :
and " m∠Q = 2x " ;
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So we plug in these values:
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→ m∠R + m∠Q = 180 ;
→ (x - 15) + 2x = 180 ;
→ x - 15 + 2x = 180 ;
→ combine the "like terms" on the "left-hand side of the equation" :
x + 2x = 1x + 2x = 3x ;
Rewrite as: 3x - 15 = 180 ;
Now add "15" to each side of the equation:
3x - 15 + 15 = 180 + 15 ;
to get:
3x = 195 ;
Now, divide each side of the equation by "3" ; to isolate "x" on the left-hand side of the equation; and to solve for " x" ;
3x / 3 = 195/3 ;
to get: x = 65 ;
Now, we are to solve for: m∡R ; which is: " (x - 15) " ;
So we substitute "65" ; for "x" ;
→ m∡R = x - 15 = 65 - 15 = 50 ;
The answer is: " m∡R = 50.°
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Note: Alternate method:
Above; when we have:
"3x - 15 = 180 " ;
we can divide each side of the equation by "3";
to get:
1x - 5 = 60 ;
→ x - 5 = 60 ;
Add "5" to each side of the equation:
x - 5 + 5 = 60 ;
→ x = 60 ;
and then continue acordingly.
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Best wishes!
