Question

find the value of x. then classify the triangle. (section 7.3)
11.
12.
13.

1. railroad crossing describe two ways to find the measure of $\angle 2$. (section 1 and section 7.2)

Explanation:

Step1: Sum of triangle angles = 180°

$x + 40 + 25 = 180$

Step2: Calculate x for Q11

$x = 180 - 40 - 25 = 115$

Step3: Right isosceles triangle angles

$x + x + 90 = 180$

Step4: Calculate x for Q12

$2x = 90 \implies x = 45$

Step5: Isosceles triangle angle sum

$(x-20) + 60 + 60 = 180$

Step6: Calculate x for Q13

$x - 20 = 60 \implies x = 80$

Step7: Method 1 for ∠2: Vertical angles

$\angle 2 = 115^\circ$ (vertical to 115° angle)

Step8: Method 2 for ∠2: Linear pair

$\angle 1 = 180 - 115 = 65^\circ$, so $\angle 2 = 180 - 65 = 115^\circ$

Answer:

1. $x=115$, Obtuse Scalene Triangle
2. $x=45$, Right Isosceles Triangle
3. $x=80$, Acute Isosceles Triangle
4. Way 1: $\angle 2$ is a vertical angle to the $115^\circ$ angle, so $m\angle 2=115^\circ$. Way 2: Use linear pairs: first find $\angle 1 = 180^\circ - 115^\circ = 65^\circ$, then $m\angle 2 = 180^\circ - 65^\circ = 115^\circ$