Question

ABCF is a parallelogram,DME,DGB AND DFC are straight lines.The measure of angle ADG-angle MDF is

Answer 1

Answer: I hope this may help you

Explanation:

Answer 2

$\angle ADG-\angle MDF=14^{\circ}$

Explanation:

ABCF is  a parallelogram

$\Angle DBC=DBE=90^{\circ}$

In triangle DBC

$\angle BCF=52^{\circ}$

$\angle C+\angle DBC+\angle CDB=180^{\circ}$

By using triangle angles sum property

Substitute the values

$52+90+\angle CDB=180$

$142+\angle CDB=180$

$\angle CDB=180-142=38^{\circ}$

In triangle DBE

$\angle DEB=72^{\circ}$

$\angle DBE+\angle DEB+\angle EDB=180$

By using triangle angles sum property

$72+90+\angle EDB=180$

$162+\angle EDB=180$

$\angle EDB=180-162=18^{\circ}$

$\angle CDE=\angle MDF=\angle CDB-\angle EDB=38-18=20^{\circ}$

Opposite angle of parallelogram are equal and sum of adjacent angles of parallelogram is equal to 180 degrees.

Therefore, $\angle BCF=\angle BAF=52^{\circ}$

$\angle DAG=56^{\circ}$

$\angle BAD=52+56=108^{\circ}$

$\angle BCF+\angle ABC=180^{\circ}$

Substitute the values

$52+90+\angle ABD=180$

$\angle ABD=180-90-52=38^{\circ}$

In triangle ABD

$\angle ADB+\angle BAD+\angle ABD=180$

By using triangle angles sum property

$108+36+\angle ADB=180$

$\angle ADB=180-108-38=34^{\circ}$

$\angle ADG=\angle ADB=34^{\circ}$

$\angle ADG-\angle MDF=34-20=14^{\circ}$

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https://brainly.in/question/12550874:Answered by Amitnrw