Question

solve with full solution in the given figure l parallel to M and PQ parallel to Rs if the measure of angle 1 is equal 100 degree find remaining angle​

Answer 1

Given:

• PQ || RS
• $\angle 1 = 100^{\circ}$
• l || m

Construction:

• Extend PQ on line m and let the angle be $\angle 7$

Since PQ is a straight line.

$\therefore \angle 1 + \angle 2 = 180^{\circ}$ ( Linear pair)

$\angle 2 = 180^{\circ} - 100^{\circ}$ ( Since, $\angle 1 = 100^{\circ}$ , given)

$\angle 2 = 80^{\circ}$ ... (1)

$\angle 3 = \angle 1$ ( Vertically Opposite angles)

$\angle 3 = 100^{\circ}$ [ Since, $\angle 1 = 100^{\circ}$ , given ]

$\angle 7 = \angle 1$ ( Corresponding angles )

$\angle 7 = 100^{\circ}$ ... (2)

$\angle 7 + \angle 6 = 180^{\circ}$ ( Sum of co-interior angles is 180°)

$\angle 6 = 180^{\circ} - 100^{\circ}$ ( $\angle 7 = 100^{\circ}$, from (2) )

$\angle 6 = 80^{\circ}$ ...(3)

$\angle 6 = \angle 5$ ( Vertically opposite angles )

$\angle 5 = 80^{\circ}$ ( from (3) )

$\angle 5 + \angle 4 = 180^{\circ}$ ( Linear pair )

$\angle 4 = 180^{\circ} - 80^{\circ}$ ( from (3) )

$\angle 4 = 100^{\circ}$