Makahanap ng eksaktong solusyon sa iyong mga problema sa IDNStudy.com. Alamin ang mga detalyadong sagot mula sa mga bihasang miyembro ng aming komunidad na sumasaklaw sa iba't ibang paksa para sa lahat ng iyong pangangailangan.
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:
- \( m \angle DLS = 72^\circ \)
- \( m \angle DUP = 72^\circ \)
- \( m \angle SUP = 193.5^\circ \)