In a diagram,pqr is a straight line,(m+n)=120 and (n+r)=100.find the value of (m+r)
If (m+n)=120 and (n+r)=100
means
m + n =120° and n + r = 100°
then
m + n + r = 180°
Since m + n = 120°
120 ° + r = 180°
r = 180° - 120°
r = 60°
n + r = 100°
n + 60° = 100°
n = 100° - 60°
n = 40°
Again
m + n + r = 180°
m + 40 ° + 60° = 180°
m + 100° = 180°
m = 180° - 100°
m = 80°
m + r = 80° + 60° = 140^
m + r = 80° + 60° = 140°
To find the value of (m+r), we need to determine the individual values of m, n, and r.
We are given two equations:
1. (m+n) = 120
2. (n+r) = 100
Let's solve these equations step by step:
From the first equation, (m+n) = 120, we can isolate m by subtracting n from both sides:
m = 120 - n
Now we have an expression for m in terms of n.
Next, we will substitute this expression for m into the second equation to solve for r:
(n+r) = 100
(120 - n + r) = 100 (substituting m = 120 - n into the equation)
Now, let's simplify the second equation:
120 - n + r = 100
To find the value of (m+r), we need to isolate (m+r) by performing further algebraic operations.
Let's start by subtracting 120 from both sides of the equation to eliminate the constant term:
- n + r = -20
Next, let's rearrange the equation by swapping the terms to put r in front of -n:
r - n = -20
Now, let's rearrange the equation to solve for (m+r):
r = -20 + n
Finally, let's substitute this expression for r back into the equation m = 120 - n:
m = 120 - n
= 120 - (-20 + n) (substituting r = -20 + n)
Simplifying further:
m = 120 + 20 - n
= 140 - n
Therefore, the value of (m+r) is equal to:
(m+r) = (140 - n) + (r)
= 140 + r - n
Since we don't have an explicit value for n or r, we cannot determine the exact value of (m+r).