Question

the figure, ABC is right angled at C, and CD AB.
Also, A = 65°. Find:
(1) ACD
(ii) BCD
(ii) CBD​

Answer 1

Explanation :

As we have given, ABC is a right angled triangle at c, so /_ACB = 90°

In triangle ADC,

/_ACD +/_CDA + /_CAD = 180°

.....(sum of the measures of angles of triangle is 180°)

/_BDC = /_CDA = 90° ,

/_CAD = 65° ......(Given)

therefore,

/_ACD + 90° + 65° = 180°

/_ACD + 155 = 180°

/_ACD = 180° - 155°

/_ACD = 25°

in the given figure, /_ACB = 90°

/_ACB = /_ACD + /_DCB

90° = 25° + /_DCB

/_DCB = 90° - 25°

/_DCB = 65 = /_BCD

in triangle CDB ,

/_CDB + /_CBD +/_BCD = 180°

90° + /_CBD + 65° = 180°

155° + /_CBD = 180°

/_CBD = 180° - 155°

/_CBD = 25°

Answer 2

Answer:

As we have given, ABC is a right angled triangle at c, so /_ACB = 90°

In triangle ADC,

/_ACD +/_CDA + /_CAD = 180°

.....(sum of the measures of angles of triangle is 180°)

/_BDC = /_CDA = 90° ,

/_CAD = 65° ......(Given)

therefore,

/_ACD + 90° + 65° = 180°

/_ACD + 155 = 180°

/_ACD = 180° - 155°

/_ACD = 25°

in the given figure, /_ACB = 90°

/_ACB = /_ACD + /_DCB

90° = 25° + /_DCB

/_DCB = 90° - 25°

/_DCB = 65 = /_BCD

in triangle CDB ,

/_CDB + /_CBD +/_BCD = 180°

90° + /_CBD + 65° = 180°

155° + /_CBD = 180°

/_CBD = 180° - 155°

/_CBD = 25°