Answer:
Angle BDA=x
Sum of int. angles=opp. ext. angle
Angle CBD=2x
Angle BCD=2x
Angle CDB=180-4x
Angle BCD=BDC
So, 2x=180-4x+x
x=36°
Measure of angle 'x' given in the picture will be 36°.
From the picture attached,
In ΔABD,
m∠DAB = x° [Given]
AB ≅ BD [Isosceles triangle]
Therefore, opposite sides of the given triangles will measure the same.
m∠BAD = m∠BDA = x°
m∠BAD + m∠BDA + m∠ABD = 180° [By triangle sum theorem]
x° + x° + m∠ABD = 180°
m∠ABD = 180°- 2x°
m∠DBC + m∠ABD = 180° [Linear pair of angles]
m∠DBC + (180° - 2x) = 180°
m∠DBC = 2x°
In isosceles ΔBCD,
BD ≅ CD
Therefore, m∠DBC = m∠BCD = 2x°
In isosceles ΔACD,
Since, AC ≅ AD,
Therefore, m∠ACD = m∠ADC = 2x°
By applying triangle sum theorem in ΔACD,
m∠ACD + m∠DAC + m∠CDA = 180°
2x° + x° + 2x° = 180°
5x° = 180°
x = 36°
Therefore, measure of 'x' will be 36°.
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