What is the value of y? A. 55° B. 850 C. 10° D. 110°

1 answer:

GaryK [48]3 years ago

5 0

I may not know I am sorry ma’am for your math problem is to hard

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DanielleElmas [232]

Answer:

135 degrees

Step-by-step explanation:

Angle CBD is the sum of angle ABC and angle ABD, so we find these first
An Isosceles triangle has 2 equal sides and 2 equal angles
Isosceles triangle theorem tells us that the 2 equal angles are respectively opposite the equal sides
Since triangle ABC has sides AB=AC, then angle ACB = angle ABC
So knowing that angles of triangle add up to 180, then
$\angle CAB+\angle ACB+\angle ABC=180\\(50)+\angle ACB+\angle ABC=180\\50-(50)+\angle ACB+\angle ABC=180-(50)\\\angle ACB+\angle ABC=130\\But,\angle ACB=\angle ABC,so\\(\angle ABC)+\angle ABC=130\\2\angle ABC=130\\\angle ABC=65$
Now we do the next triangle to get ABD
Since triangle ABD has sides AB=BD, then angle BDA = angle BAD
So knowing that angles of triangle add up to 180, then
$\angle BDA+\angle BAD+\angle ABD=180\\(55)+\angle BAD+\angle ABD=180\\But,\angle BDA=\angle BAD,so\\(55)+(55)+\angle ABD=180\\110+\angle ABD=180\\110-(110)+\angle ABD=180-(110)\\\angle ABD=70$
Now we said, angle CBD is the sum of angle ABC and angle ABD, so
$\angle ABC+\angle ABD=\angle CBD\\(65)+(70)=\angle CBD\\\angle CBD=135$