Question

ABCD is a cyclic quadrilateral. If angle BCD = 100° and angle ABD = 70°, find angle ADB​

Answer 1

${\huge{\underbrace{\rm{Question}}}}$

ABCD is a cyclic quadrilateral. If angle BCD = 100° and angle ABD = 70°, find angle ADB

${\huge{\underbrace{\rm{Answer}}}}$

Given:

ABCD is a cyclic quadrilateral

angle BCD = 100°

angle ABD = 70°

To find:

find angle ADB

Solution:

□ ABCD is a cyclic quadrilateral

$\red\bigstar$ We know that, sum of opposite angles is 180°

.°. Angle DAB + Angle BCD = 180°

⟹ Angle DAB + 100° = 180°

⟹ Angle DAB = 180° – 100°

.°. Angle DAB = 80°

Now,

We also know that,

$\blue\bigstar$ the sum of all angles of a triangle is 180°

In ∆ ABD ,

⟹ Angle ADB + Angle DBA + Angel BAD = 180°

⟹ Angle ADB + 70° + 80° = 180°

⟹ Angle ADB = 180° – 80° – 70°

$\boxed{\bf{\pink{.°.\:Angle\:ADB \:=\:30°}}}$

Therefore, angle ADB = 30°

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer 2

Given:

ABCD is a cyclic quadrilateral

angle BCD = 100°

angle ABD = 70°

To find:

find angle ADB

Solution:

□ ABCD is a cyclic quadrilateral

★ We know that, sum of opposite angles is 180°

.°. Angle DAB + Angle BCD = 180°

⟹ Angle DAB + 100° = 180°

⟹ Angle DAB = 180° – 100°

.°. Angle DAB = 80°

Now,

We also know that,

★ the sum of all angles of a triangle is 180°

In ∆ ABD ,

⟹ Angle ADB + Angle DBA + Angel BAD = 180°

⟹ Angle ADB + 70° + 80° = 180°

⟹ Angle ADB = 180° – 80° – 70°

Therefore, angle ADB = 30°