Question

Question 105(ii)

In the given PQ, RS and UT are parallel lines.

If c $={75}^{\circ }anda=\frac{2}{5}c,$ find b.

Answer 1

Since, $PQ||UTandPT$ is transversal.
Therefore,$\angle QPT=\angle UTP\left[alternateinteriorangles\right]\Rightarrow a+b=c\Rightarrow b=c-a\Rightarrow b=c-\frac{2}{5}c[\therefore a=\frac{2c}{5},given]\Rightarrow b=\frac{5c-2c}{5}\Rightarrow b=\frac{3c}{5}\Rightarrow b=\frac{3\times {75}^{\circ }}{5}[\therefore c={75}^{\circ }]\Rightarrow b={45}^{\circ }$