THE TRIANGLE AND ITS PROPERTIES
298401
In Fig. if AB || CD, the values of x and y are:
4
1 x = 21, y = 28
2 x = 21, y = 38
3 x = 38, y = 21
4 x = 22, y = 38
Explanation:
x = 21, y = 38
\(\angle \text{AEC}+\angle \text{AEB}=180^\circ\) [Linear angles]
\(\Rightarrow 79^\circ+\angle \text{AEB}=180^\circ\)
\(\Rightarrow \angle \text{AEB}=101^\circ\)
Since, AB || CD
\(\angle \text{ABE}=\angle \text{ECD}=58^\circ\) [Alternate angles]
Now, In \(\triangle \text{AEB}\)
\(\angle \text{AEB}+\angle \text{EAB}+\angle \text{ABE}=180^\circ\) [Angle sum property of triangle]
\(\Rightarrow 101^\circ+58^\circ+\text{x}^\circ=180^\circ\)
\(\Rightarrow \text{x}^\circ=21^\circ\)
\(\Rightarrow \text{x}=21\)
Now, In \(\triangle \text{AEB}\)
\(\angle \text{AEC}+\angle \text{CAE}+\angle \text{CEA}=180^\circ\) [Angle sum property of triangle]
\(\Rightarrow 79^\circ+\text{y}^\circ+3\text{x}^\circ=180^\circ\)
\(\Rightarrow 79^\circ+\text{y}^\circ+3(21)^\circ=180^\circ\)
\(\Rightarrow 79^\circ+\text{y}^\circ+63^\circ=180^\circ\)
\(\Rightarrow \text{y}^\circ=38^\circ\)
\(\Rightarrow \text{y}=38\)
Hence, the correct answer is option (b).