Given that ∠a≅∠b , evelia conjectured that ∠a and ∠b are acute angles. which statement is a counterexample to evelia's conjecture?
(high school)
m∠a=114° and m∠b=170°

m∠a=126° and m∠b=126°

m∠a=30° and m∠b=40°

m∠a=45° and m∠b=45°

B

Step-by-step explanation:

Given that ∠A ≅ ∠B, Evelia conjectured that ∠A and ∠B are acute angles.

Consider all options:

A. If m∠A=114° and m∠B=170°, then angles A and B are not congruent, so this is not a counterexample.

B. If m∠A=126° and m∠B=126°, then angles A and B are congruent and both these angles are obtuse (their measures are greater than 90°). This means that two obtuse angles can be congruent, so this is a counterexample. True option.

C.  If m∠A=30° and m∠B=40°, then angles A and B are not congruent, so this is not a counterexample.

D. If m∠A=45° and m∠B=45°, then angles A and B are congruent, so this examples show two congruent acute angles. But if we have to prove some statement, we have to prove this statement for an arbitrary angles, not for one pair of angles. Moreover, this is an example illustrating given statement, but is not a counterexample.

a=r

d=q

c=p

b=s

hope this !

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."