Question

find the value of x in this​

Answer 1

Answer:

x° = 40°

Step-by-step explanation:

Given: Angle ACE = 130° ,

DC = DA = DB

Angle ABD = x°

To Find: x°

Solution:

>> Angle ACD + Angle ACE = 180° [Linear Pair]

>> Angle ACD + 130 = 180

>> Angle ACD = 180 - 130

>> Angle ACD = 50°

In ∆ADC:

>> DC = DA

>> Angle CAD = Angle ACD [Isosceles Triangle Property]

>> Angle CAD = 50°

In ∆ADC:

>> Angle ACD + Angle CAD + Angle ADC = 180° [Angle Sum Property]

>> 50 + 50 + Angle ADC = 180°

>> Angle ADC = 180 - 100

>> Angle ADC = 80°

>> Angle ADC + Angle ADB = 180° [Linear Pair]

>> 80 + Angle ADB = 180°

>> Angle ADB = 180 - 80

>> Angle ADB = 100°

In ∆ADB:

>> DA = DB

>> Angle ABD = Angle BAD [Isosceles Triangle Property]

In ∆ADB:

>> Angle ABD + Angle BAD + Angle ADB = 180° [Angle Sum Property]

>> Angle ABD + Angle ABD + 100 = 180

>> 2 Angle ABD + 100 = 180

>> 2 Angle ABD = 180 - 100

>> 2 Angle ABD = 80

>> Angle ABD = 80/2

>> Angle ABD = 40°

.°. x° = 40°

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