Questions: 180-54=126 126/2=63 x=67 180.75=105 105/2=52.5 x=52.5 180-70=110/2=55 x=55

Transcript text: \[ \left\{\begin{array}{l} 180-54=126 \\ \frac{126}{2}=63 \\ x=67 \end{array}\right. \] \[ \left\{\begin{array}{l} 180.75=105 \\ \frac{105}{2}=52.5 \\ x=52.5 \end{array}\right. \] \[ \begin{array}{c} 180-70=\frac{110}{2}=55 \\ x-55 \end{array} \]

Solution

Solution Steps

Step 1: Isosceles Triangle Theorem

The given triangle has two congruent sides, marked with single dashes. Therefore, the angles opposite those sides are congruent. Since one angle is labeled _x_, the other angle is also _x_. The third angle is labeled 7. The sum of the angles in a triangle is 180°.

x + x + 7 = 180 2x + 7 = 180 2x = 173 x = 7

Step 2: Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two remote interior angles. In this problem, the exterior angle is labeled _x_, and the two remote interior angles are 7 and 6.

x = 7 + 6 x = 13

Step 3: Sum of Angles in a Triangle

The sum of the angles in a triangle is 180°. The angles in this triangle are labeled x+6, 3x-1, and 5x-3.

(x + 6) + (3x - 1) + (5x - 3) = 180 9x + 2 = 180 9x = 178 x ≈ 19.8