What is the value of y?

Mathematics

1 answer:

Amiraneli [1.4K]3 years ago

5 0

Answer:

$\boxed{D. \: 40\degree}$

Step-by-step explanation:

<em>Angle sum property of triangle states that the sum of interior angles of a triangle is 180°</em>

So,

$= > 2y \degree + (y + 10)\degree + 50\degree = 180\degree \\ \\ = > 2y\degree + y\degree + 10\degree + 50\degree = 180\degree \\ \\ = > 3y\degree + 60\degree = 180\degree \\ \\ = > 3y\degree = 180\degree - 60\degree \\ \\ = > 3y\degree = 120\degree \\ \\ = > y = \frac{120\degree}{3\degree} \\ \\ = > y = 40\degree$

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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
$\angle ABC+\angle ABD=\angle CBD\\(65)+(70)=\angle CBD\\\angle CBD=135$