Q. 35.0( 1 Vote )

# In the figu

Answer :

We have Angle sum property of triangles states that the sum of angles in a triangle is always 180°.

In ∆ABC,

By Angle Sum Property of triangles, we get

ABC + BCA + CAB = 180°

90° + BCA + CAB = 180° [ it is given that, ABC = 90°]

BCA + CAB = 180° - 90°

BCA + CAB = 90° …(i)

In ∆ADC,

By Angle Sum Property of triangles, we get

ADC + ACD + CAD = 180° …(ii)

In ∆ACE,

By Angle Sum Property of triangles, we get

ACE + CAE + AEC = 180° …(iii)

Adding equations (ii) and (iii), we get

(ADC + ACD + CAD) + (ACE + EAC + AEC) = 180° + 180° [ AD and CE are the bisectors of angles A and C respectively]      ADC + ACE + (3 × 45°) = 360°

ADC + ACE + 135° = 360°

ADC + ACE = 360° - 135°

ADC + ACE = 225°

Thus, ADC + ACE = 225°

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