Question

1. (2 - 122) identify the geometric angle - relationship(s) in each diagram. use what you know about those relationships to write an equation and solve for x.

a.
b.
name shyla hoy
period 3
closure for chapters 1 and 2
geometry (20 points)

Explanation:

Step1: Identify angle - relationship in part a

The two angles \(x + 15^{\circ}\) and \(105^{\circ}\) are supplementary (linear - pair), so their sum is \(180^{\circ}\). The equation is \((x + 15)+105=180\).

Step2: Solve the equation for \(x\) in part a

First, simplify the left - hand side of the equation: \(x+15 + 105=x + 120\). So, \(x+120 = 180\). Subtract 120 from both sides: \(x=180 - 120\), and \(x = 60\).

Step3: Identify angle - relationship in part b

In an isosceles triangle, the two base angles are equal. Let the base angles be equal. The sum of the interior angles of a triangle is \(180^{\circ}\). So the equation is \(2(2x-6)+(2x - 6)=180\).

Step4: Solve the equation for \(x\) in part b

First, expand the left - hand side: \(4x-12 + 2x-6=180\). Combine like terms: \(6x-18 = 180\). Add 18 to both sides: \(6x=180 + 18=198\). Divide both sides by 6: \(x=\frac{198}{6}=33\).

Answer:

a. \(x = 60\)
b. \(x = 33\)