triangles independent practice write and solve an equation to find the measures of each angle in the triangles shown below. | triangle | equation and work | angle measures | | --- | --- | --- | | 1. | _________________ | ∠a= _____
∠b= _____
∠c= _____ | | 2. | _________________ | ∠d= _____
∠e= _____
∠f= _____ | | 3. $\isosceles$ | _________________ | ∠g= _____
∠h= _____
∠i= _____ | | 4. | _________________ | ∠j= _____
∠k= _____
∠l= _____ | 5. ∠m and ∠n are supplementary and ( mangle m = 37^circ ). if ( mangle n = (13x)^circ ), what is the value of ( x ) and the ( mangle n )?
a. equation: _________________
b. ( x = _____ ), ( mangle m _____ ), ( mangle n _____ ) 6. which angle pairs form complementary angles?
$\angle$

Question

triangles independent practice write and solve an equation to find the measures of each angle in the triangles shown below. | triangle | equation and work | angle measures | | --- | --- | --- | | 1. riangle

| _________________ | ∠a= _____
∠b= _____
∠c= _____ | | 2. riangle

| _________________ | ∠d= _____
∠e= _____
∠f= _____ | | 3. $\isosceles$ | _________________ | ∠g= _____
∠h= _____
∠i= _____ | | 4. riangle

| _________________ | ∠j= _____
∠k= _____
∠l= _____ | 5. ∠m and ∠n are supplementary and ( mangle m = 37^circ ). if ( mangle n = (13x)^circ ), what is the value of ( x ) and the ( mangle n )?
a. equation: _________________
b. ( x = _____ ), ( mangle m _____ ), ( mangle n _____ ) 6. which angle pairs form complementary angles?
$\angle$

Accepted Answer

### Problem 1: Triangle ABC
# Explanation:
## Step1: Recall triangle angle sum (180°)
The sum of angles in a triangle is $ 180^\circ $. So, $ \angle A + \angle B + \angle C = 180^\circ $. Substituting the given angles: $ (2x + 8) + 63 + (x + 7) = 180 $.

## Step2: Simplify and solve for $ x $
Combine like terms: $ 2x + 8 + 63 + x + 7 = 180 $ → $ 3x + 78 = 180 $. Subtract 78: $ 3x = 102 $ → $ x = 34 $.

## Step3: Find each angle
- $ \angle A = 2x + 8 = 2(34) + 8 = 76^\circ $
- $ \angle B = 63^\circ $ (given)
- $ \angle C = x + 7 = 34 + 7 = 41^\circ $

# Answer:
$ \angle A = 76^\circ $, $ \angle B = 63^\circ $, $ \angle C = 41^\circ $

### Problem 2: Triangle DEF
# Explanation:
## Step1: Triangle angle sum (180°)
$ \angle D + \angle E + \angle F = 180^\circ $. Substitute: $ (x + 20) + 3x + 36 = 180 $.

## Step2: Solve for $ x $
Combine terms: $ 4x + 56 = 180 $. Subtract 56: $ 4x = 124 $ → $ x = 31 $.

## Step3: Calculate angles
- $ \angle D = x + 20 = 31 + 20 = 51^\circ $
- $ \angle E = 3x = 3(31) = 93^\circ $
- $ \angle F = 36^\circ $ (given)

# Answer:
$ \angle D = 51^\circ $, $ \angle E = 93^\circ $, $ \angle F = 36^\circ $

### Problem 3: Triangle GHI (Isosceles, $ GH = GI $)
# Explanation:
## Step1: Isosceles triangle (equal base angles)
Since $ GH = GI $, $ \angle H = \angle I = x^\circ $. Angle sum: $ 28 + x + x = 180 $.

## Step2: Solve for $ x $
$ 2x + 28 = 180 $ → $ 2x = 152 $ → $ x = 76 $.

## Step3: Angles
- $ \angle G = 28^\circ $ (given)
- $ \angle H = 76^\circ $
- $ \angle I = 76^\circ $

# Answer:
$ \angle G = 28^\circ $, $ \angle H = 76^\circ $, $ \angle I = 76^\circ $

### Problem 4: Triangle JKL
# Explanation:
## Step1: Triangle angle sum (180°)
$ \angle J + \angle K + \angle L = 180^\circ $. Substitute: $ 41 + (5x - 5) + 3x = 180 $.

## Step2: Solve for $ x $
Combine terms: $ 8x + 36 = 180 $. Subtract 36: $ 8x = 144 $ → $ x = 18 $.

## Step3: Find angles
- $ \angle J = 41^\circ $ (given)
- $ \angle K = 5x - 5 = 5(18) - 5 = 85^\circ $
- $ \angle L = 3x = 3(18) = 54^\circ $

# Answer:
$ \angle J = 41^\circ $, $ \angle K = 85^\circ $, $ \angle L = 54^\circ $

### Problem 5: Supplementary Angles $ \angle M $ and $ \angle N $
# Explanation:
## Step1: Supplementary angles sum to 180°
$ m\angle M + m\angle N = 180^\circ $. Given $ m\angle M = 37^\circ $, $ m\angle N = 13x $. So, $ 37 + 13x = 180 $.

## Step2: Solve for $ x $
Subtract 37: $ 13x = 143 $ → $ x = 11 $.

## Step3: Find $ m\angle N $
$ m\angle N = 13x = 13(11) = 143^\circ $.

# Answer:
$ x = 11 $, $ m\angle N = 143^\circ $

### Problem 6: Complementary Angles (Sum to 90°)
# Explanation:
Check pairs:
- $ 25^\circ + 65^\circ = 90^\circ $ (angles at B: $ 25^\circ $ and $ 65^\circ $)
- $ 50^\circ + 40^\circ = 90^\circ $ (angles at B: $ 50^\circ $ and $ 40^\circ $)

# Answer:
Angle pairs: $ 25^\circ $ & $ 65^\circ $, $ 50^\circ $ & $ 40^\circ $ (e.g., $ \angle ABE $ & $ \angle EBF $, $ \angle DBE $ & $ \angle FBC $)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: Triangle ABC

Step1: Recall triangle angle sum (180°)

Step2: Simplify and solve for \( x \)

Step3: Find each angle

Step1: Triangle angle sum (180°)

Step2: Solve for \( x \)

Step3: Calculate angles

Step1: Isosceles triangle (equal base angles)

Step2: Solve for \( x \)

Step3: Angles

Answer:

Problem 2: Triangle DEF

triangle	equation and work	angle measures
2. <img src=\triangle2.png\ alt=\triangle with vertices d, e, f. angle at d is (x + 20)°, angle at e is (3x)°, angle at f is 36°\>	_________________	∠d= ___<br>∠e= _<br>∠f= ___
3. <img src=\triangle3.png\ alt=\isosceles triangle with vertices g, h, i. angle at g is 28°, angle at h is x°, sides gh and gi are equal? wait, no, sides gh and hi? wait, the triangle has markings on gh and hi? wait, the image shows triangle ghi with angle at g 28°, and sides gh and hi marked as equal? wait, maybe its isosceles with gh = hi? so angles at g and i? wait, no, the angle at h is x°.>	_________________	∠g= ___<br>∠h= _<br>∠i= ___
4. <img src=\triangle4.png\ alt=\triangle with vertices j, k, l. angle at j is 41°, angle at k is (5x - 5)°, angle at l is (3x)°\>	_________________	∠j= ___<br>∠k= _<br>∠l= ___