Question

1. (1 point each) in the accompanying diagram, $overline{cb}$ intersects $overline{da}$ at point $o$. if $mangle coa = 114^{circ}$, find: (a) $mangle aob$ (b) $mangle dob$ (c) $mangle cod$

Explanation:

Step1: Use linear - pair property for ∠AOB

∠COA and ∠AOB form a linear pair. The sum of angles in a linear pair is 180°.
$m\angle AOB=180^{\circ}-m\angle COA$
$m\angle AOB = 180 - 114=66^{\circ}$

Step2: Use vertical - angles property for ∠DOB

Vertical angles are equal. ∠DOB and ∠COA are vertical angles.
$m\angle DOB=m\angle COA = 114^{\circ}$

Step3: Use vertical - angles property for ∠COD

∠COD and ∠AOB are vertical angles.
$m\angle COD=m\angle AOB = 66^{\circ}$

Answer:

(a) $m\angle AOB = 66^{\circ}$
(b) $m\angle DOB = 114^{\circ}$
(c) $m\angle COD = 66^{\circ}$