Question

In the given figure,I || m and t is a transversal.If | 5 = 70°, find the measure of each
the angles.
​

Answer 1

Answer:

you can also browse this question on Google

Answer 2

Step-by-step explanation:

As line l || m and t is transversal,

$\red{ \text{\( \therefore \: \: \angle 1=\angle 5=70^{\circ} \) [Corresspoding angles are equal]}}$

$\color{purple} \pmb{ \text{ \( \angle 1=\angle 3=70^{\circ} \quad \) [vertically opposite angles are equal]}}$

$\color{darkviolet} \pmb{ \text{ \( \angle 3=\angle 7=70^{\circ} \) [Corresspoding angles are equal]}}$

$\color{maroon} \pmb{ \tt\therefore \angle 1=\angle 3=\angle 5=\angle 7=70^{\circ} }$

$\color{darkcyan} \pmb{ \begin{array}{} \text{We know, the sum of linear pair angles is } \text{\( 180^{\circ} \)} \\ \text{ \( \angle 1+\angle 2=180^{\circ} \) } \\ \text{\( \Rightarrow 70^{\circ}+\angle 2=180^{\circ} \) } \\ \text{\( \Rightarrow \angle 2=180^{\circ}-70^{\circ} \)} \\ \text{ \( \Rightarrow \angle 2=110^{\circ} \) } \\ \text{Now, \( \angle 2=\angle 4=110^{\circ} \) [Corresspoding angles are equal]} \\ \text{ \( \angle 2=\angle 4=110^{\circ} \) [vertically opposite angles are equal]} \\ \text{ \( \angle 4=\angle 8=110^{\circ}[ \) Corresspoding angles are equal] } \\ \text{\( \therefore \angle 2=\angle 4=\angle 6=\angle 8=110^{\circ} . \)} \\ \text{ Hence, \( \angle 1=\angle 3=\angle 5=\angle 7=70^{\circ} \) and \( \angle 2=\angle 4=\angle 6=\angle 8=110^{\circ} . \)} \end{array}}$