If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)°, then the ratio of these angles is

Options

A. `1 : 3`
B. `2 : 3`
C. `1 : 4`
D. `1 : 2`

Answer

To solve the problem, we need to find the ratio of two adjacent angles of a parallelogram given as (5x - 5)° and (10x + 35)°. Let's go through the solution step by step.

### Step 1: Use the property of adjacent angles in a parallelogram
In a parallelogram, the sum of two adjacent angles is always 180°. Therefore, we can set up the equation:
\[ (5x - 5) + (10x + 35) = 180 \]

### Step 2: Simplify the equation
Combine like terms:
\[ 5x - 5 + 10x + 35 = 180 \]
This simplifies to:
\[ 15x + 30 = 180 \]

### Step 3: Isolate the variable
Subtract 30 from both sides to isolate the term with x:
\[ 15x = 180 - 30 \]
This gives:
\[ 15x = 150 \]

### Step 4: Solve for x
Now, divide both sides by 15 to find the value of x:
\[ x = \frac{150}{15} = 10 \]

### Step 5: Calculate the angles
Now that we have the value of x, we can find the measures of the two angles.

**First angle:**
\[ 5x - 5 = 5(10) - 5 = 50 - 5 = 45° \]

**Second angle:**
\[ 10x + 35 = 10(10) + 35 = 100 + 35 = 135° \]

### Step 6: Find the ratio of the two angles
Now we can find the ratio of the two angles:
\[ \text{Ratio} = \frac{45}{135} \]

### Step 7: Simplify the ratio
To simplify the ratio, we can divide both the numerator and the denominator by 45:
\[ \frac{45 \div 45}{135 \div 45} = \frac{1}{3} \]

Thus, the ratio of the two adjacent angles is:
\[ 1 : 3 \]

### Final Answer:
The ratio of the angles (5x - 5)° and (10x + 35)° is **1 : 3**.

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