38. exterior angle theorem
∠1 + ∠2 = ___
a) 180
b) 90
c)

Question

38. exterior angle theorem
∠1 + ∠2 = ___
a) 180
b) 90
c) <4
d) <3
the exterior angle theorem states that...
39. find x.
triangle with angles 110°, 25°, and x
a) 85
b) 95
c) 35
d) 45
40. find the value of x.
triangle with side 3x+2, angle 70°, and exterior angle 9x+6
a) 6
b) 4
c) 11
d) 5
41. find the measure of the missing angle.
triangle with angles 20°, 130°, and?
a) 40°
b) 30°
c) 150°
d) 110°

Accepted Answer

### Problem 39: Find $ x $
# Explanation:
## Step 1: Recall Triangle Angle Sum
The sum of angles in a triangle is $ 180^\circ $. So, $ x + 110^\circ + 25^\circ = 180^\circ $.
## Step 2: Solve for $ x $
Simplify: $ x + 135^\circ = 180^\circ $. Subtract $ 135^\circ $: $ x = 180^\circ - 135^\circ = 45^\circ $? Wait, no—wait, the options have 45? Wait, no, let's check again. Wait, maybe it's an exterior angle? Wait, no, the triangle has angles $ x $, $ 110^\circ $, $ 25^\circ $. Wait, $ 110 + 25 = 135 $, $ 180 - 135 = 45 $. But the options: a)85, b)95, c)35, d)45. Oh, d)45. Wait, maybe I miscalculated. Wait, no—wait, maybe it's an exterior angle? Wait, no, the diagram shows a triangle with angles $ x $, $ 25^\circ $, and $ 110^\circ $. So sum is $ 180 $. So $ x = 180 - 110 - 25 = 45 $. So answer is d)45.

# Answer:
d) 45

### Problem 41: Find the missing angle
# Explanation:
## Step 1: Triangle Angle Sum
Sum of angles in a triangle is $ 180^\circ $. Given angles: $ 20^\circ $, $ 130^\circ $, and missing angle $ y $.
## Step 2: Calculate $ y $
$ 20 + 130 + y = 180 $. $ 150 + y = 180 $. $ y = 180 - 150 = 30^\circ $. So option b)30°.

# Answer:
b) 30°

### Problem 40: Find $ x $
# Explanation:
## Step 1: Exterior Angle Theorem
Exterior angle = sum of two remote interior angles. So $ 9x + 6 = (3x + 2) + 70 $.
## Step 2: Solve Equation
Simplify: $ 9x + 6 = 3x + 72 $. Subtract $ 3x $: $ 6x + 6 = 72 $. Subtract 6: $ 6x = 66 $. Divide by 6: $ x = 11 $. But options are A)6, B)4, C)11, D)5. So C)11.

# Answer:
C) 11

### Problem 38: Exterior Angle Theorem
# Explanation:
The Exterior Angle Theorem states that the exterior angle ($ \angle 4 $) is equal to the sum of the two non-adjacent interior angles ($ \angle 1 + \angle 2 $). So $ \angle 1 + \angle 2 = \angle 4 $, but the options: a)180, b)90, c)<4, d)<3. Wait, no—wait, the question is $ \angle 1 + \angle 2 = $ __. The Exterior Angle Theorem says $ \angle 1 + \angle 2 = \angle 4 $, but the options given: a)180, b)90, c)<4, d)<3. Wait, maybe the options are miswritten. Wait, the Exterior Angle Theorem: the exterior angle is equal to the sum of the two remote interior angles. So $ \angle 1 + \angle 2 = \angle 4 $, but if $ \angle 3 + \angle 4 = 180 $ (linear pair), but the question is $ \angle 1 + \angle 2 = $ __. Wait, maybe the options are wrong, but the correct answer based on the theorem is that $ \angle 1 + \angle 2 = \angle 4 $, but the options have c)<4? No, that doesn't make sense. Wait, maybe the question is "The Exterior Angle Theorem states that $ \angle 1 + \angle 2 = $ __", and the options are a)180, b)90, c)$ \angle 4 $, d)$ \angle 3 $. But in the given options, c) is <4, which is likely a typo. Assuming the correct option is that $ \angle 1 + \angle 2 = \angle 4 $, but the options have c)<4, which is incorrect. Wait, maybe the original question has a typo, but based on the theorem, the exterior angle is equal to the sum of the two remote interior angles, so $ \angle 1 + \angle 2 = \angle 4 $. But the options given: a)180, b)90, c)<4, d)<3. This is confusing. Maybe the question is "The Exterior Angle Theorem states that $ \angle 1 + \angle 2 $ is equal to...", and the correct answer is that it's equal to the exterior angle ($ \angle 4 $), but the options are misprinted. Alternatively, maybe the question is about the sum of interior angles, but no. Given the options, maybe the intended answer is c) (assuming <4 is a typo for $ \angle 4 $), but this is unclear. However, based on the theorem, the correct relation is $ \angle 1 + \angle 2 = \angle 4 $, so if c) is $ \angle 4 $ (but written as <4), maybe that's the answer.

# Answer:
c) <4 (assuming typo for $ \angle 4 $)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 39: Find \( x \)

Step 1: Recall Triangle Angle Sum

Step 2: Solve for \( x \)

Step 1: Triangle Angle Sum

Step 2: Calculate \( y \)

Step 1: Exterior Angle Theorem

Step 2: Solve Equation

Answer:

Problem 41: Find the missing angle