The measures of two angles of a quadrilateral are `115^(@) and 45^(@)`, and the other two angles are equal. Find the measure of each of the equal angles.

Options

A. `120^(@)`
B. `105^(@)`
C. `100^(@)`
D. `130^(@)`

Answer

To find the measure of each of the equal angles in the quadrilateral, we can follow these steps:

### Step 1: Understand the properties of a quadrilateral
The sum of all interior angles in a quadrilateral is always 360 degrees.

### Step 2: Identify the known angles
We know two angles of the quadrilateral:
- Angle A = 115 degrees
- Angle B = 45 degrees

### Step 3: Set up the equation for the unknown angles
Let the measure of each of the equal angles (Angle C and Angle D) be represented as \( x \). Therefore, we can express the sum of the angles as:
\[ \text{Angle A} + \text{Angle B} + \text{Angle C} + \text{Angle D} = 360^\circ \]
Substituting the known values:
\[ 115 + 45 + x + x = 360 \]

### Step 4: Simplify the equation
Combine the known angles:
\[ 115 + 45 = 160 \]
So the equation becomes:
\[ 160 + 2x = 360 \]

### Step 5: Solve for \( x \)
To isolate \( 2x \), subtract 160 from both sides:
\[ 2x = 360 - 160 \]
\[ 2x = 200 \]
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{200}{2} \]
\[ x = 100 \]

### Step 6: Conclusion
Thus, the measure of each of the equal angles (Angle C and Angle D) is:
\[ \text{Angle C} = 100^\circ \quad \text{and} \quad \text{Angle D} = 100^\circ \]

### Final Answer:
Each of the equal angles measures \( 100^\circ \).

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