The sum of two angles of a triangle is 95 and their difference is 25. ...
SUM OF ALL THE ANGLES OF A TRIANGLE=180 DEGREES
ANGLE 1+ANGLE 2=95 DEGREES
ANGLE 1-ANGLE 2=25 DEGREES
MEASURE OF ANGLE 1=60 DEGREES
MEASURE OF ANGLE 2=35 DEGREES
MEASURE OF ANGLE 3=180 DEGREES-95 DEGREES
=85 DEGREES
THEREFORE, THE MEASURE OF THE THIRD ANGLE IS 85 DEGREES.
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The sum of two angles of a triangle is 95 and their difference is 25. ...
Problem: The sum of two angles of a triangle is 95 and their difference is 25. Find the third angle?
Solution:
To solve this problem, we need to use the properties of triangles and the relationships between their angles.
Step 1: Understand the problem:
We are given two pieces of information about the angles of a triangle:
- The sum of two angles is 95.
- The difference between the same two angles is 25.
We need to find the measure of the third angle.
Step 2: Identify the key information:
Let's assign variables to the angles of the triangle:
- Let A be the first angle.
- Let B be the second angle.
- Let C be the third angle.
From the given information, we can write two equations:
- A + B = 95
- A - B = 25
Step 3: Solve the equations:
We can solve these two equations using the method of elimination or substitution. Let's use the method of substitution.
From the second equation, we can rearrange it to express A in terms of B:
A = B + 25
Substituting this value of A in the first equation, we get:
(B + 25) + B = 95
2B + 25 = 95
2B = 95 - 25
2B = 70
B = 70/2
B = 35
Now that we have the value of B, we can substitute it back into one of the original equations to find the value of A:
A + 35 = 95
A = 95 - 35
A = 60
Step 4: Find the third angle:
To find the measure of the third angle, we can subtract the sum of the first two angles from 180 degrees (since the angles of a triangle add up to 180 degrees):
C = 180 - (A + B)
C = 180 - (60 + 35)
C = 180 - 95
C = 85
Therefore, the measure of the third angle is 85 degrees.
Step 5: Check the answer:
To verify our answer, we can check if the sum of all three angles is indeed 180 degrees:
A + B + C = 60 + 35 + 85 = 180
Since the sum is equal to 180, our answer is correct.
Conclusion:
The third angle of the triangle is 85 degrees.
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