I need help please !

Question

asked Jan 27, 2022 202k views

1 Answer

Elvy · Answer 1 · 2022-02-01T04:12:44+0000

Answer:

See Explanation

Explanation:

$\overrightarrow{KH} \: bisects \: \angle GKJ$ (Given)

$\therefore \angle GKH \cong \angle HKJ$ (angle bisector theorem)

$\therefore m\angle GKH = m\angle HKJ$

$\implies m \angle 11 =m \angle 12$

$m\angle 9 + m\angle 12 = 180\degree.... (1)$ (Linear pair angles)

&

$m\angle 10 + m\angle 11 = 180\degree$ (Linear pair angles)

$\implies m\angle 10 + m\angle 12 = 180\degree.... (2)$
$(\because m \angle 11 = m\angle 12)$

From equations (1) & (2)

$m\angle 9 + \cancel {m\angle 12} =m\angle 10 + \cancel {m\angle 12}$

$\therefore m\angle 9 =m\angle 10$

$\implies \huge \orange {\angle 9 \cong \angle 10}$

Thus proved