Question

if an angle is twice its supplement, the angle is ____ degrees.
select one:
a. 60
b. 120
c. 30
d. 5

if an acute angle increases, then its supplement
select one:
a. not enough information
b. decreases
c. stays the same
d. increases

Explanation:

Step1: Define variables for first problem

Let the supplement be $x$, the angle be $2x$.

Step2: Use supplementary angle property

Supplementary angles sum to $180^\circ$:
$$x + 2x = 180^\circ$$

Step3: Solve for $x$

$$3x = 180^\circ \implies x = 60^\circ$$

Step4: Find the target angle

The angle is $2x = 2\times60^\circ = 120^\circ$

Step5: Analyze second problem logic

Supplementary angles sum to $180^\circ$. If an acute angle $\theta$ increases, its supplement is $180^\circ - \theta$, so it decreases.

Answer:

1. b. 120
2. b. decreases