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The sum of two angles of a triangle is 95 and their difference is 25. Find the third angle?
Most Upvoted Answer
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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Community Answer
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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The sum of two angles of a triangle is 95 and their difference is 25. Find the third angle? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The sum of two angles of a triangle is 95 and their difference is 25. Find the third angle? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of two angles of a triangle is 95 and their difference is 25. Find the third angle?.
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