`angleP` and `angleQ` are supplementary angles such that `angleP=2x-5` and `angleQ=3x+10`. Then, find `angleQ.`

Options

A. `35^(@)`
B. `65^(@)`
C. `105^(@)`
D. `115^(@)`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the concept of supplementary angles
Supplementary angles are two angles whose sum is equal to 180 degrees. Therefore, we can set up the equation:
\[ \text{angle P} + \text{angle Q} = 180^\circ \]

### Step 2: Substitute the expressions for angle P and angle Q
We are given:
- \(\text{angle P} = 2x - 5\)
- \(\text{angle Q} = 3x + 10\)

Substituting these into the equation gives us:
\[ (2x - 5) + (3x + 10) = 180 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 2x + 3x - 5 + 10 = 180 \]
This simplifies to:
\[ 5x + 5 = 180 \]

### Step 4: Isolate the variable x
Subtract 5 from both sides:
\[ 5x = 180 - 5 \]
\[ 5x = 175 \]

### Step 5: Solve for x
Divide both sides by 5:
\[ x = \frac{175}{5} = 35 \]

### Step 6: Find angle Q
Now that we have the value of \(x\), we can substitute it back into the expression for angle Q:
\[ \text{angle Q} = 3x + 10 \]
Substituting \(x = 35\):
\[ \text{angle Q} = 3(35) + 10 \]
\[ \text{angle Q} = 105 + 10 = 115^\circ \]

### Final Answer
Thus, the measure of angle Q is:
\[ \text{angle Q} = 115^\circ \]

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