One of the angles of a triangle is `110^(@)` and the other two angles are equal. What is the measure of each of these equal angles?

Options

A. `37^(@)`
B. `35^(@)`
C. `70^(@)`
D. `75^(@)`

Answer

To solve the problem step by step, let's follow the reasoning laid out in the video transcript:

### Step 1: Understand the properties of a triangle
The sum of all angles in a triangle is always 180 degrees.

### Step 2: Identify the known angle
We know one angle of the triangle is 110 degrees. Let's denote this angle as Angle A.

### Step 3: Set up the equation for the unknown angles
Let the other two angles be equal, and we can denote them as Angle B and Angle C. Since they are equal, we can say:
- Angle B = Angle C = x (where x is the measure of each of these equal angles)

### Step 4: Write the equation for the sum of angles
According to the property of triangles, we can write the equation:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]
Substituting the known values:
\[ 110^\circ + x + x = 180^\circ \]

### Step 5: Simplify the equation
This simplifies to:
\[ 110^\circ + 2x = 180^\circ \]

### Step 6: Solve for x
To isolate x, we first subtract 110 degrees from both sides:
\[ 2x = 180^\circ - 110^\circ \]
\[ 2x = 70^\circ \]

Now, divide both sides by 2:
\[ x = \frac{70^\circ}{2} \]
\[ x = 35^\circ \]

### Step 7: Conclusion
Thus, the measure of each of the equal angles (Angle B and Angle C) is 35 degrees.

### Final Answer:
Angle B = 35 degrees, Angle C = 35 degrees.

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