Question

1. which proof method starts by assuming the opposite of what needs to be proven?

a. indirect proof
b. flowchart proof
c. two - column proof
d. paragraph proof

1. an angle ∠abc is bisected, and the measure of one of the bisected angles is given by 5x - 3°. if the full angle ∠abc = 154°, what is the value of x?

a. 28°
b. 23°
c. 16°
d. 25°

1. in parallelogram efgh, the measure of ∠f = 100°. what is the measure of ∠g?

a. 40°
b. 100°
c. 80°
d. 130°

Explanation:

4.

Indirect proof, also known as proof by contradiction, starts by assuming the opposite of what needs to be proven and then showing that this assumption leads to a contradiction.

Step1: Recall angle - bisector property

An angle bisector divides an angle into two equal parts. So if $\angle ABC$ is bisected and one of the bisected angles is $5x - 3^{\circ}$, then $2(5x - 3)=154$.

Step2: Expand the left - hand side

$10x-6 = 154$.

Step3: Add 6 to both sides

$10x=154 + 6=160$.

Step4: Solve for x

$x=\frac{160}{10}=16$.

Step1: Recall properties of a parallelogram

In a parallelogram, adjacent angles are supplementary, that is, they add up to $180^{\circ}$. $\angle F$ and $\angle G$ are adjacent angles in parallelogram $EFGH$.

Step2: Set up the equation

$\angle F+\angle G = 180^{\circ}$. Given $\angle F = 100^{\circ}$, then $100^{\circ}+\angle G=180^{\circ}$.

Step3: Solve for $\angle G$

$\angle G=180^{\circ}-100^{\circ}=80^{\circ}$.

Answer:

A. Indirect proof

5.