In a rhombus ABCD, measure of angle CAB is` 25^@`. What is the measure of angle ABC?

Options

A. `65^@`
B. `50^@`
C. `40^@`
D. `130^@`

Answer

To find the measure of angle ABC in rhombus ABCD, where the measure of angle CAB is given as 25 degrees, we can follow these steps:

### Step 1: Understand the properties of a rhombus
A rhombus has the following properties:
- All sides are equal in length.
- Opposite angles are equal.
- Adjacent angles are supplementary (they add up to 180 degrees).

### Step 2: Identify the angles
In rhombus ABCD, we have:
- Angle CAB = 25 degrees (given).
- Since AB = BC (sides of the rhombus), angle ABC (which we need to find) will also be equal to angle CAB.

### Step 3: Use the property of opposite angles
Since opposite angles are equal in a rhombus:
- Angle ABC = Angle CAB = 25 degrees.

### Step 4: Find angle ACB
Now, we can find angle ACB using the property of supplementary angles:
- Angle CAB + Angle ABC + Angle ACB = 180 degrees.
- Let angle ACB = x.
- Therefore, 25 + 25 + x = 180.
- This simplifies to 50 + x = 180.
- Solving for x gives us x = 180 - 50 = 130 degrees.

### Step 5: Conclusion
Thus, the measure of angle ABC is 130 degrees.

### Final Answer:
Angle ABC = 130 degrees.

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