IDNStudy.com, kung saan ang iyong mga tanong ay may malinaw na sagot. Ang aming mga eksperto ay nagbibigay ng mabilis at eksaktong sagot upang tulungan kang maunawaan at malutas ang anumang problema.
Answer:
To solve for \( m \) (angle measures), let's interpret the given information and solve step by step:
Given:
- \( m \angle DLS = 72^\circ \)
- \( m \angle DUP = 72^\circ \)
- \( m \angle DUP = 2x + 15 \)
- \( m \angle SUP = 7x - 6 \)
First, equate \( m \angle DUP \) to \( 72^\circ \):
\[ 2x + 15 = 72 \]
Subtract 15 from both sides:
\[ 2x = 72 - 15 \]
\[ 2x = 57 \]
Divide both sides by 2 to solve for \( x \):
\[ x = \frac{57}{2} \]
\[ x = 28.5 \]
Now that we have \( x \), substitute it back into \( m \angle SUP \) to find \( m \angle SUP \):
\[ m \angle SUP = 7x - 6 \]
\[ m \angle SUP = 7(28.5) - 6 \]
\[ m \angle SUP = 199.5 - 6 \]
\[ m \angle SUP = 193.5 \]
So, \( m \angle SUP = 193.5^\circ \).
Next, substitute \( x \) into \( m \angle DUP \) to find \( m \angle DUP \):
\[ m \angle DUP = 2x + 15 \]
\[ m \angle DUP = 2(28.5) + 15 \]
\[ m \angle DUP = 57 + 15 \]
\[ m \angle DUP = 72 \]
So, \( m \angle DUP = 72^\circ \).
Therefore, the angle measures are:
- \( m \angle DLS = 72^\circ \)
- \( m \angle DUP = 72^\circ \)
- \( m \angle SUP = 193.5^\circ \)