In ΔRST,
R
T
‾
RT
is extended through point T to point U,
m
∠
R
S
T
=
(
3
x
+
17
)
∘
m∠RST=(3x+17)
∘
,
m
∠
S
T
U
=
(
8
x
+
1
)
∘
m∠STU=(8x+1)
∘
, and
m
∠
T
R
S
=
(
3
x
+
18
)
∘
m∠TRS=(3x+18)
∘
. What is the value of
x
?
x?
We know that the sum of angles in a triangle is 180 degrees, so:
m∠RST + m∠STU + m∠TRS = 180
Substituting the given angle measures, we get:
(3x+17) + (8x+1) + (3x+18) = 180
Simplifying this equation, we get:
14x + 36 = 180
Solving for x, we get:
x = 11
Therefore, the value of x is 11.
To find the value of x, we can use the angle-angle-angle (AAA) similarity criterion. The criterion states that if two triangles have corresponding angles that are congruent, then the triangles are similar.
In triangle RST, we have three angles:
m∠RST = 3x + 17°
m∠STU = 8x + 1°
m∠TRS = 3x + 18°
Since the angles in a triangle add up to 180°, we can sum up the three angles in triangle RST:
(3x + 17) + (8x + 1) + (3x + 18) = 180
Simplifying the equation:
14x + 36 = 180
Next, we can solve for x:
14x = 180 - 36
14x = 144
x = 144/14
x = 10.29
Therefore, the value of x is approximately 10.29.