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Rufina [12.5K]
3 years ago
7

Please solve these questions for me. i am having a difficult time understanding.

Mathematics
1 answer:
s2008m [1.1K]3 years ago
8 0

Answer:

1) AD=BC(corresponding parts of congruent triangles)

2)The value of x and y are 65 ° and 77.5° respectively

Step-by-step explanation:

1)

Given : AD||BC

AC bisects BD

So, AE=EC and BE=ED

We need to prove AD = BC

In ΔAED and ΔBEC

AE=EC (Given)

\angle AED = \angel BEC ( Vertically opposite angles)

BE=ED (Given)

So, ΔAED ≅ ΔBEC (By SAS)

So, AD=BC(corresponding parts of congruent triangles)

Hence Proved

2)

Refer the attached figure

\angle ABC = 90^{\circ}

In ΔDBC

BC=DC (Given)

So,\angle CDB=\angle DBC(Opposite angles of equal sides are equal)

So,\angle CDB=\angle DBC=x

So,\angle CDB+\angle DBC+\angle BCD = 180^{\circ} (Angle sum property)

x+x+50=180

2x+50=180

2x=130

x=65

So,\angle CDB=\angle DBC=x = 65^{\circ}

Now,

\angle ABC = 90^{\circ}\\\angle ABC=\angle ABD+\angle DBC=\angle ABD+x=90

So,\angle ABD=90-x=90-65=25^{\circ}

In ΔABD

AB = BD (Given)

So,\angle BAD=\angle BDA(Opposite angles of equal sides are equal)

So,\angle BAD=\angle BDA=y

So,\angle BAD+\angle BDA+\angle ABD = 180^{\circ}(Angle Sum property)

y+y+25=180

2y=180-25

2y=155

y=77.5

So, The value of x and y are 65 ° and 77.5° respectively

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