Question

Answer for a lot of points!

Answer 1

Given :

• ZC = 90°

• CD is the altitude to AB.

• $\angle$A = 65°.

To find :

• the angles in △CBD and △CAD if m∠A = 65°

Solution :

In Right angle △ABC,

we have,

=> ACB = 90°

=> $\angle$CAB = 65°.

So,

=> $\angle$ACB + $\angle$CAB+$\angle$ZCBA = 180° (By angle sum Property.)

=> 90° + 65° + $\angle$CBA = 180°

=> 155° +$\angle$CBA = 180°

=> $\angle$CBA = 180° - 155°

=> $\angle$CBA = 25°.

In △CDB,

=> CD is the altitude to AB.

So,

=> $\angle$ CDB = 90°

=> $\angle$CBD = $\angle$CBA = 25°.

So,

=> $\angle$CBD + $\angle$DCB = 180° (Angle sum Property.)

=> 90° +25° + $\angle$DCB = 180°

=> 115° + $\angle$DCB = 180°

=> $\angle$DCB = 180° - 115°

=> $\angle$DCB = 65°.

Now, in △ADC,

=> CD is the altitude to AB.

So,

=> $\angle$ADC = 90°

=>$\angle$ CAD =$\angle$ CAB = 65°.

So,

=> $\angle$ADC + $\angle$CAD +$\angle$DCA = 180° (Angle sum Property.)

=> 90° + 65° + $\angle$DCA = 180°

=> 155° +$\angle$DCA = 180°

=> $\angle$DCA = 180° - 155°

=> $\angle$DCA = 25°

Hence, we get,

• $\angle$DCA = 25°
• $\angle$DCB = 65°
• $\angle$CDB = 90°
• $\angle$ACD = 25°
• $\angle$ADC = 90°.