Question

How to solve this pls tell step by step....

Answer 1

Answer:

Angle DOC=120degree(By Sum of all the interior angle of a triangle).

Angle ABC=140degree(By Sum of all the interior angle of a quadrilateral).

Answer 2

Answer:

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Step-by-step explanation:

In figure, DO and CO are the bisectors of ∠ADC and ∠BCD respectively. If ∠ADC = ∠BCD = 60° and ∠DAB = 100°, find the measures of ∠DOC and ∠ABC.

solving :

we knew that the sum of the interior angles of a triangle is 180°

i.e ,

In ∆ DOC

=>∠D+∠C+∠O = 180°

=>30°+30°+∠O = 180°

=>60°+∠O = 180°

=>∠O = 180°-60°

=>∠O = 120° = ∠DOC

we know that the the sum of the interior angles of the quadrilateral is 360°

and the

Angle Bisector theorem :

In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.

then according to angle Bisector theorem ,

In □ ABCD :

=>∠D = 30 x 2 = 60°

=>∠ C = 30 x 2 = 60°

=>∠D = 60° = ∠C

FROM angle sum property of the quadrilateral

∠A +∠B +∠C +∠D = 360°

Given ∠A =100° then

∠A +∠B +∠C +∠D = 360°

=> 100° + ∠B + 60° +60° = 360°

=> 220°+∠B = 360°

=> ∠B = 360° -220°

=> ∠B = 140° = ∠ABC

therefore ∠DOC = 120° and ∠ABC = 140°