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 w
hat could be the measure of the other acute angle?
2 answers:
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°
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