Question

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

Answer 1

Answer:

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=$30\°$

Step-by-step 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=$30\°$