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In isosceles triangleABC, one angle meas...

In isosceles triangleABC, one angle measure `55^(@)` and another angle measure `70^(@)`. Which one of the following is the measure of the third angle?

A

`40`

B

`55`

C

`70`

D

It cannot be determined from the information given.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the measure of the third angle in the isosceles triangle ABC, given that one angle measures 55 degrees and another angle measures 70 degrees. ### Step-by-Step Solution: 1. **Understand the properties of a triangle**: The sum of the angles in any triangle is always 180 degrees. 2. **Set up the equation**: Let the measure of the third angle be \( x \). According to the angle sum property, we can write the equation: \[ 55 + 70 + x = 180 \] 3. **Combine the known angles**: Add the two known angles together: \[ 55 + 70 = 125 \] So the equation now looks like: \[ 125 + x = 180 \] 4. **Solve for \( x \)**: To find \( x \), subtract 125 from both sides of the equation: \[ x = 180 - 125 \] \[ x = 55 \] 5. **Conclusion**: The measure of the third angle \( x \) is 55 degrees. ### Final Answer: The measure of the third angle is \( 55^\circ \).
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