Question

Lines AB and CD intersect each other at point O. If angle AOC : angle COB = 5 : 7, find all angles. 
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Answer 1

Step-by-step explanation:

As the Line AB is a straight line Then angle AOC and angle COB must be a linear pair i.e. their sum = 180°

Lets take a constant X in the ratio

5x:7x

This implies 5x+7x =180

12x= 180

X = 15

So the angles are 75° and 105°

angle COB = Angle AOD ( Vertically opposite angles)

So angle AOD is 105° and the rest is 75 °

Hope it helps

Thank you

Answer 2

given ;

AOC :COB= 5x:7x

to find ;

angle , AOC, COB, BOD, DOA

proof ;

AB is a straight line ,so

AOC+COB = 180°

$5x + 7x = 180 \\ \\ 12x = 180 \\ x = 15$

AOC = 5x

$5 \times 15 \\ = 75$

and , COB = 7x

$7 \times 15 = 105$

angle AOC= DOB = 75° [ by vertical opposite angle ]

angle COB = DOA = 105° [ by vertical opposite angle ]