two angles of a triangle are m° and (m+20)°.their sum is greater than the third angle.find the range value of m
The third angle = 180° - m - ( m + 20° ) = 180° - m - m - 20° = 160° - 2 m
Sum sum is greater than the third angle mean:
m + m + 20° > 160° - 2 m
Now:
2 m + 20° > 160° - 2 m
2 m + 2 m > 160° - 20°
4 m > 140°
m > 140° / 4
m > 35°
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To find the range of possible values for angle m, we need to consider the conditions given in the question.
In a triangle, the sum of all angles is always 180°. Therefore, we can set up the equation:
m° + (m+20)° + x° = 180°
Where x° represents the measure of the third angle.
From the given conditions, we also know that the sum of the two given angles is greater than the third angle. Mathematically, this can be expressed as:
m° + (m+20)° > x°
Let's solve these two equations to find the range of values for m:
1. Solve the equation m° + (m+20)° + x° = 180° for x°:
Combine like terms:
2m + 20 + x = 180
Subtract 20 from both sides:
2m + x = 160
Subtract 2m from both sides:
x = 160 - 2m
2. Solve the inequality m° + (m+20)° > x°:
Substitute the value of x from the first equation:
m + (m+20) > 160 - 2m
Simplify:
2m + 20 > 160 - 2m
Add 2m to both sides:
4m + 20 > 160
Subtract 20 from both sides:
4m > 140
Divide both sides by 4:
m > 35
Therefore, the range of values for m is m > 35.