Question

find the missing angles​

Answer 1

Sum of all angles = 180

(3x-7)+55+(x+20)=180

4x+55+20-7=180

4x+68=180

4x= 180-68

4x= 112

x= 112/4 = 28

x=28

angle AOC= 3*28-7

=77

angle BOD= 28+20

=48

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Answer 2

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Understanding Concept:

As we can see, that AB is a straight line and OC and OD are intersecting AB. This divides the line AB into 3 parts. AOC, COD & DOB.

The sum of all angles of a straight line is 180^{\circ} .

Solution:

$Angle AOB + Angle COD + Angle DOB = 180^{\circ} \\:\implies (3x - 7) + (55) + (x + 20) = 180\\:\implies 3x - 7 + 55 + x + 20 = 180\\:\implies 4x + 68 = 180\\:\implies 4x = 112 \\:\implies x = \dfrac{112}{4}\\:\implies x = 28. \\\\:\implies The\:missing\:angles\:are-: \\\bf{1) 3x - 7 => 3(28) - 7 => 84 - 7 => 77^{\circ}} \\\bf{2) x + 20 => 28 + 20 => 48^{\circ}}$

Verifications:

$Angle AOB + Angle COD + Angle DOB = 180^{\circ} \\:\implies 77^{\circ} + 55^{\circ} + 48^{\circ} = 180^{\circ} \\:\implies 180^{\circ} = 180^{\circ} \\LHS=RHS. \\ HENCE\:\:\:VERIFIED$

HOPE IT HELPS!!!