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# If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown

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If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown [#permalink]
Quote:
If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown above, then what is the value of xº?

<BAC=<BCA=45

<BCA+<ACD=90

<ACD + <ADC + <DAC = 180
<DAC =90

Please hit kudos if you liked the solution! Cheers
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Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown [#permalink]
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Since triangle ABC is isoceles, angle A = angle C = 45
Since BCD is 90, then the remaining angle = 45
Since ADC is isoceles, x = 180-(45*2) = 90 D
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If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown [#permalink]
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Bunuel wrote:

If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown above, then what is the value of xº?

A. 30º
B. 45º
C. 60º
D. 90º
E. 105º

Project PS Butler

Attachment:
The attachment 1.png is no longer available

IMO D, Follow the attachment steps.

Posted from my mobile device
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IMG_20210706_130842.jpg [ 38.69 KiB | Viewed 1807 times ]

IMG_20210706_130546.jpg [ 6.42 KiB | Viewed 1811 times ]

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Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown [#permalink]
2
Kudos
Bunuel wrote:

If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown above, then what is the value of xº?

A. 30º
B. 45º
C. 60º
D. 90º
E. 105º

Project PS Butler

Attachment:
1.png

Clearly, <BAC = <BCA = 45 each
<BCA = <ACD = <ADC = 40 each
x + 90 = 180
x = 90 (D), IMO!
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Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown [#permalink]
3
Kudos
Triangle ABC forms a isosceles right triangle since side AB and BC are equal. Hence Angle A=Angle C=(180-B)/2= (180-90)/2=45 degrees

Now in Triangle ADC, Angle C=90-45=45 degrees.
Since AD=AC Triangle ADC forms isosceles triangle with angles opposite to equal sides measuring 45 degrees each.
So angle x measures 180-(45+45)=90 degrees.

IMO option (d) is the correct answer.
Re: If AB = BC, DA = AC, and angles DCB and ABC are right angles as shown [#permalink]
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