Question

Geometry isosceles and equilateral triangles find the value of x in each diagram

Answer 1

Part 9)
`x=12`

Part 10)
`x=12\°`

Part 11)
`x=10\°`

Part 12)
`x=11\°`

Part 13)

a)
`SU=4\ units`

b) m∠VWX=
`40\°`

c) m∠WVX=
`50\°`

d) m∠XTV=
`60\°`

e) m∠XVT=
`30\°`

Explanation:

Part 9) we have that

`12=2x-12` ----->by SSA

solve for x

`2x=24`

`x=12`

Part 10)

In the isosceles triangle of the left the vertex angle is equal to

`180\°-68\°*2=44\°`

Find the measure of angle 2

m∠2=
`90\°-44\°=46\°`

m∠2=
`4x-2`

`4x-2=46\°`

solve for x

`4x=48\°`

`x=12\°`

Part 11)

Find the base angle in the isosceles triangle of the top

`180\°-118\°=62\°`

Find the vertex angle in the isosceles triangle of the top

`180\°-2*62\°=56\°`

Find the vertex angle 2 in the isosceles triangle of the bottom

`180\°-56\°=124\°` ------> this is the measure of angle 2

m∠2=
`124\°`

m∠2=
`12x+4`

`12x+4=124\°`

`12x=120\°`

`x=10\°`

Part 12)

m∠2=
`146\°` ------> by corresponding angles

m∠2=
`13x+3`

`13x+3=146\°`

`13x=143\°`

`x=11\°`

Part 13)

a) we have that

SU=UW ------> given problem

`3x+1=x+3`

`2x=2`

`x=1`

therefore

`SU=3x+1=3+1=4`

`SU=4\ units`

b) we know that

m∠VWX=
`4y\°`

in the right triangle UVW find the value of y

The sum of the internal angles of a triangle is equal to
`180\°`

so

`180\°=4y+90\°+50\°`

`180\°=4y+140\°`

`4y=40\°`

`y=10\°`

so

m∠VWX=
`4y\°=40\°`

Part c) we know that

in the right triangle VWX

The sum of the internal angles of a triangle is equal to
`180\°`

so

m∠WVX=
`180\°-(4y+90\°)`

m∠WVX=
`180\°-(40\°+90\°)`

m∠WVX=
`50\°`

Part d) we know that

in the right triangle XTV

The sum of the internal angles of a triangle is equal to
`180\°`

so

m∠XTV=
`180\°-(40\°-y+90\°)`

m∠XTV=
`180\°-(40\°-10\°+90\°)`

m∠XTV=
`60\°`

Part e) we know that

m∠XVT=
`(40\°-y)`

substitute the value of y

m∠XVT=
`(40\°-10\°)`

m∠XVT=
`30\°`