Question
The diagram shows a triangle.
3p
2p
45°
What is the value of p?
p =
°
3p
2p
45°
What is the value of p?
p =
°
Answers
GPT-4o mini
To solve for \( p \) in the triangle described, we can use the information provided, which includes angles of the triangle.
The angles of a triangle sum up to \( 180^\circ \). In the triangle, we have one angle given as \( 45^\circ \), another angle as \( 3p \), and the last angle as \( 2p \). We can set up the equation as follows:
\[
3p + 2p + 45^\circ = 180^\circ
\]
Now, let's combine the terms involving \( p \):
\[
5p + 45^\circ = 180^\circ
\]
Next, we will isolate \( 5p \) by subtracting \( 45^\circ \) from both sides:
\[
5p = 180^\circ - 45^\circ
\]
\[
5p = 135^\circ
\]
Now, we can solve for \( p \) by dividing both sides by 5:
\[
p = \frac{135^\circ}{5} = 27^\circ
\]
Thus, the value of \( p \) is:
\[
\boxed{27^\circ}
\]
The angles of a triangle sum up to \( 180^\circ \). In the triangle, we have one angle given as \( 45^\circ \), another angle as \( 3p \), and the last angle as \( 2p \). We can set up the equation as follows:
\[
3p + 2p + 45^\circ = 180^\circ
\]
Now, let's combine the terms involving \( p \):
\[
5p + 45^\circ = 180^\circ
\]
Next, we will isolate \( 5p \) by subtracting \( 45^\circ \) from both sides:
\[
5p = 180^\circ - 45^\circ
\]
\[
5p = 135^\circ
\]
Now, we can solve for \( p \) by dividing both sides by 5:
\[
p = \frac{135^\circ}{5} = 27^\circ
\]
Thus, the value of \( p \) is:
\[
\boxed{27^\circ}
\]