Question

question image
x + 80
x + 50
72°
q 1. write an equation to find the value of x in the triangle. 2. find the value of x.3. find the measurement of angle a.

Explanation:

Part 1: Write an equation to find \( x \)

Step1: Recall triangle angle sum

The sum of angles in a triangle is \( 180^\circ \). So, add the three angles: \( (x + 50) + (x + 80) + 72 = 180 \).

Step2: Simplify the left - hand side

Combine like terms: \( x + 50+x + 80+72=2x + 202 \). So the equation is \( 2x+202 = 180 \).

Part 2: Find the value of \( x \)

Step1: Subtract 202 from both sides

Starting with \( 2x+202 = 180 \), subtract 202 from each side: \( 2x=180 - 202=- 22 \). Wait, this seems incorrect. Wait, maybe I made a mistake in adding the angles. Wait, let's re - check. The three angles are \( (x + 50) \), \( (x + 80) \) and \( 72^\circ \). So sum is \( (x + 50)+(x + 80)+72=2x+(50 + 80+72)=2x + 202 \). But if \( 2x+202 = 180 \), then \( 2x=180 - 202=-22 \), \( x=- 11 \). But angles can't be negative. Wait, maybe the angle labels are different. Wait, maybe the triangle is labeled differently. Wait, perhaps the angle \( A \) is one of the angles, but let's assume that the sum of angles in a triangle is \( 180^\circ \), so the correct equation is \( (x + 50)+(x + 80)+72 = 180 \). Let's solve it again.

Step1: Combine like terms

\( x+50+x + 80+72=2x+202 \), so \( 2x+202 = 180 \)

Step2: Subtract 202 from both sides

\( 2x=180 - 202=-22 \)

Step3: Divide by 2

\( x=\frac{-22}{2}=- 11 \)

Wait, this gives a negative value for \( x \), which would make \( x + 50=39^\circ \) and \( x + 80 = 69^\circ \), and \( 39+69 + 72=180 \). Oh, right, even though \( x \) is negative, the angles are positive. So \( x=-11 \).

Part 3: Find the measurement of angle \( A \)

Assuming angle \( A \) is one of the angles. Let's assume angle \( A \) is \( x + 50 \) or \( x + 80 \). If angle \( A=x + 50 \), then \( A=-11 + 50 = 39^\circ \). If angle \( A=x + 80 \), then \( A=-11+80 = 69^\circ \). If angle \( A = 72^\circ \), then it's \( 72^\circ \). But since the problem says "angle \( A \)", and from the diagram, let's assume angle \( A \) is \( x + 50 \) (the smallest angle). So \( A = 39^\circ \).

Answer:

s:

1. The equation is \( (x + 50)+(x + 80)+72=180 \) (or simplified as \( 2x + 202=180 \))
2. The value of \( x=-11 \)
3. If angle \( A=x + 50 \), then the measurement of angle \( A = 39^\circ \); if angle \( A=x + 80 \), then \( A = 69^\circ \); if angle \( A = 72^\circ \), then \( A = 72^\circ \) (assuming the labeling, the most probable is if angle \( A \) is \( x + 50 \), then \( 39^\circ \))