Question

In ΔOPQ, m ∠ � = ( 2 � − 5 ) ∘ m∠O=(2x−5) ∘ , m ∠ � = ( 3 � − 8 ) ∘ m∠P=(3x−8) ∘ , and m ∠ � = ( 10 � − 17 ) ∘ m∠Q=(10x−17) ∘ . What is the value of � ? x?

Answer 1

Answer:

The value of ∠� is 23 degrees, and the value of x is 14.

Explanation:

Since ∠O, ∠P, and ∠Q are angles of triangle OPQ, their sum must be 180 degrees. Therefore, we can set up the following equation:

m∠O + m∠P + m∠Q = 180

Substituting the given expressions, we get:

(2x - 5) + (3x - 8) + (10x - 17) = 180

Simplifying the left side, we get:

15x - 30 = 180

Adding 30 to both sides, we get:

15x = 210

Dividing both sides by 15, we get:

x = 14

Now we can find the value of ∠� by substituting x = 14 into the expression for m∠O:

m∠O = 2x - 5 = 2(14) - 5 = 23

Therefore, the value of ∠� is 23 degrees, and the value of x is 14.

Answer 2

Answer: Since the angles in a triangle sum up to 180 degrees, we can write:

m∠O + m∠P + m∠Q = 180

Substituting the given angle measures, we get:

(2x - 5) + (3x - 8) + (10x - 17) = 180

Simplifying and solving for x, we have:

15x - 30 = 180

15x = 210

x = 14

Now that we know x = 14, we can find the value of angle θ by substituting x into one of the angle measures:

m∠O = 2x - 5 = 2(14) - 5 = 23 degrees

Therefore, the value of angle θ is 23 degrees and the value of x is 14.

Step-by-step explanation: hope this helps (: