Question

find m∠qrp.
(19b + 15)°
(23b + 3)°

Explanation:

Step1: Use the property of corresponding angles

Since \( LM\parallel SQ\), \(\angle LJK\) and \(\angle SRP\) are corresponding angles. And \(\angle SRP\) and \(\angle QRP\) form a linear - pair. So \((19b + 15)+(23b+3)=180\).
$$19b+15 + 23b+3=180$$

Step2: Simplify the equation

Combine like terms: \(19b+23b+15 + 3=180\), \(42b+18 = 180\).
Subtract 18 from both sides: \(42b=180 - 18\), \(42b=162\).
Divide both sides by 42: \(b=\frac{162}{42}=\frac{27}{7}\).

Step3: Calculate \(\angle QRP\)

Substitute \(b = \frac{27}{7}\) into \(\angle QRP=(23b + 3)\)
\(\angle QRP=23\times\frac{27}{7}+3=\frac{621}{7}+\frac{21}{7}=\frac{621 + 21}{7}=\frac{642}{7}\approx91.71^{\circ}\)

Answer:

\(\frac{642}{7}\approx91.71^{\circ}\)