Find the angles p, q, r and s.
A)
P Q R S \[{{45}^{o}}\] \[{{50}^{o}}\] \[{{65}^{o}}\] \[{{50}^{o}}\]
B)
P Q R S \[{{45}^{o}}\] \[{{65}^{o}}\] \[{{50}^{o}}\] \[{{50}^{o}}\]
C)
P Q R S \[{{45}^{o}}\] \[{{65}^{o}}\] \[{{50}^{o}}\] \[{{65}^{o}}\]
D)
P Q R S \[{{45}^{o}}\] \[{{50}^{o}}\] \[{{65}^{o}}\] \[{{65}^{o}}\]
Correct Answer: A
Solution :
In \[\Delta ABC,\] \[r={{180}^{o}}-{{50}^{o}}-{{65}^{o}}={{65}^{o}}\] \[HC||AB\Rightarrow q={{50}^{o}}\]. (Alternate angles) \[s=q\] (Vertically opposite angles) Hence, Since BCF is a straight line, \[p+{{20}^{o}}+q+r={{180}^{o}}\Rightarrow p={{45}^{o}}\] \[\therefore \] \[p={{45}^{o}},\,q={{50}^{o}},\,r={{65}^{o}}\] and \[s={{50}^{o}}\] are the required values.
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