r06.core.learn.edgenuity.com rolled_1206310Y_Geometry_S1andS2_2016 Triangle Angle Theorems Pre-Test Active 1 2 3 4 5 6 7 8 9 10 S 35° P Q R 58° What is the value of x? x = 23 x = 35 x = 58 x = 93 Mark this and return Save and Exit Submit
The Correct Answer and Explanation is:
To solve the problem and determine the value of x, we need to apply the Triangle Angle Sum Theorem, which states:
The sum of the interior angles of a triangle is always 180°.
Given:
In triangle PQR:
∠P = 35°
∠Q = 58°
∠R = x (unknown)
Step 1: Set up the equation using the angle sum theorem:
∠P+∠Q+∠R=180∘\angle P + \angle Q + \angle R = 180^\circ 35∘+58∘+x=180∘35^\circ + 58^\circ + x = 180^\circ
Step 2: Simplify the known values:
93∘+x=180∘93^\circ + x = 180^\circ
Step 3: Solve for x:
x=180∘−93∘=87∘x = 180^\circ – 93^\circ = 87^\circ
But wait! The provided answer choices are:
x = 23
x = 35
x = 58
x = 93
None of these match 87°, so it’s likely that you may have misread or miswritten the problem.
Let’s reconsider: you wrote:
“S 35° P Q R 58°”
This suggests that maybe point S is outside triangle PQR, or there’s a diagram that is not included.
However, if the triangle has:
One angle = 35°
Another = 58°
The third = x
Then we still follow the same logic: 35∘+58∘=93∘⇒x=180∘−93∘=87∘35^\circ + 58^\circ = 93^\circ \Rightarrow x = 180^\circ – 93^\circ = 87^\circ
So x = 87° is the correct answer, not listed among the choices, meaning either:
There’s a typo or misreading, or
**You are identifying x as an exterior angle.
If x is an exterior angle to the triangle at vertex R (with interior angles 35° and 58° adjacent), then: x=35∘+58∘=93∘x = 35^\circ + 58^\circ = 93^\circ
In that case, the correct answer is:
✅ x = 93
Explanation:
To find the value of x in triangle angle problems, we use the Triangle Angle Sum Theorem, which says the interior angles of any triangle always add up to 180 degrees. This basic rule of geometry allows us to solve for unknown angles when two of the three are given. In this case, we are told two angles: 35° and 58°. Adding these gives 93°, and subtracting from 180° gives 87°, which would be the third interior angle.
However, if x is an exterior angle, the rule changes. An exterior angle of a triangle equals the sum of the two opposite interior angles (not adjacent to it). So, if x is the exterior angle at vertex R, then x = ∠P + ∠Q = 35° + 58° = 93°. This fits one of the answer choices and is the correct interpretation if x is outside the triangle at vertex R.
Understanding the context—whether an angle is interior or exterior—is crucial in solving triangle problems correctly. Geometry often involves diagrams to clarify which angle is in question. Without a diagram, we must infer based on standard conventions or clues in the text. Therefore, the correct answer is:
✅ x = 93, because it is the exterior angle formed by extending one side of the triangle.
