Question

9/9 triangle angle sum theorem
you try!!!

1. triangle with angles 85°, 50°, and x (with equation 85 + 50 + x = 180, 135 + x = 180, x = 45)
2. triangle with angles 55°, 54°, and x+74 (with equation 55 + 54 + x + 74 = 180, 183 + x = 180, x = -3)
3. triangle with angles 70°, 60°, and 8x+2

multiple-choice question
what is the value of x and the value of the missing angle for question 3?
options:
3, 25
8, 50
180
5, 42

Explanation:

Step1: Recall Triangle Angle Sum Theorem

The sum of angles in a triangle is \(180^\circ\). For question 3, the angles are \(70^\circ\), \(60^\circ\), and \(8x + 2\). So, we set up the equation: \(70 + 60 + (8x + 2)=180\).

Step2: Simplify the left - hand side

First, add the constant terms: \(70+60 + 2=132\). The equation becomes \(132+8x = 180\).

Step3: Solve for x

Subtract 132 from both sides: \(8x=180 - 132\). Calculate \(180 - 132 = 48\), so \(8x = 48\). Then divide both sides by 8: \(x=\frac{48}{8}=6\).

Step4: Find the missing angle

Substitute \(x = 6\) into \(8x + 2\): \(8\times6+2=48 + 2=50\).

Answer:

6, 50 (corresponding to the option "6, 50")