(3x-29) degrees (x+63) degrees The measure of two angles are given in algebraic form. Use the diagram to determine the value of x and the find the measure of the two angles.
 


Part A:

What is the value of x?
A.x = 92
B.x = 63
C.x = 29
D.x = 46
1b. 
Part B:

What are the measures of the angles?
A.46°
B.72°
C.109°
D.119°
Time

To determine the value of \( x \) and the measures of the two angles, let's break this down into steps. It seems the two angles, \( (3x - 29)^\circ \) and \( (x + 63)^\circ \), are related in some way. Typically, angles in problems like these are either complementary (sum to 90°), supplementary (sum to 180°), or equal (in some congruence problems). 

Let's assume they are **supplementary**, meaning their sum is 180°, which is common in diagrams where two angles form a straight line.

### Step 1: Set up the equation
\[
(3x - 29) + (x + 63) = 180
\]

### Step 2: Combine like terms
\[
3x - 29 + x + 63 = 180
\]
\[
4x + 34 = 180
\]

### Step 3: Solve for \( x \)
\[
4x = 180 - 34
\]
\[
4x = 146
\]
\[
x = \frac{146}{4}
\]
\[
x = 36.5
\]

### Step 4: Find the measures of the angles
Substitute \( x = 36.5 \) into the expressions for the angles:
- First angle: \( 3x - 29 = 3(36.5) - 29 = 109.5 - 29 = 80.5^\circ \)
- Second angle: \( x + 63 = 36.5 + 63 = 99.5^\circ \)

However, none of these match the answer choices exactly. Could you clarify the relationship between the angles (supplementary, complementary, or equal)? Or provide the diagram for better context? This will help refine the solution.

Would you like me to walk through another assumption or check the problem further?

The measure of two angles are given in algebraic form: (3x - 29) degrees and (x + 63) degrees. Use the diagram to determine the value of x and find the measure of the two angles.

This problem involves finding the value of x and the measures of two supplementary angles given in algebraic form: (3x - 29) degrees and (x + 63) degrees. Learn how to apply algebraic methods and the supplementary angles theorem to solve this step by step. Suitable for students in Grades 8-10.

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