Question

Triangles ABD, CBD and ADC are all isosceles. Find the angle x.
AC = AD

Answer 1

Step-by-step explanation:

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°.