Question

two nonoverlapping acute angles that share a ray form an obtuse angle if one of the acute angles have a a measure of 50 degres what could be the measure of the other acute angle?

Answer 1

Answer:

The measure of other acute angle has to be less than 40°

Step-by-step explanation:

Let a and b denote the two acute angle that is formed by a same ray.

such that a=50 degree.

Let c be the obtuse angle that is formed.

i.e. m∠c >90°

So, we get a triangle such that the three angles of a triangle are a , b and c.

As we know that the sum of all the angles of a triangle is 180°.

Hence,

m∠a+m∠b+m∠c=180°

Hence,

50+m∠b+m∠c=180°

m∠b+m∠c=180°-50°

m∠b+m∠c=130°

Hence,

m∠b=130°-m∠c

As,

m∠c>90°

⇒    -m∠c<-90°

⇒   130°-m∠c<130°-90°

⇒  130°-m∠c<40°

⇒  m∠b<40°

Hence, the measure of the other acute angle has to be less than 40°

Answer 2

Since anything over 90 degrees is considered obtuse the measure of the other angle could be anything over 40 degrees since 40+50=90