Answer:
Therefore the measure of the angles of a right angled triangle ABC are,
[tex]\angle A=35\°\\\angle B= 90\°\\\angle C= 55\°[/tex]
Step-by-step explanation:
Let the Common multiple be ' x '
given the angles are in the ratio 7 : 18 : 11
Therefore the angles are
∠A = 7x , ∠B = 18x , ∠C = 11x
To Find:
∠A = ? , ∠B = ? , ∠C =?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
[tex]\angle A+\angle B+\angle C=180\°[/tex] ..Triangle sum property.
Substituting the values we get
[tex]7x+18x+11x=180\\36x=180\\x=\dfrac{180}{36}=5\\\\x=5[/tex]
substitute ' x ' in the measure angles we get
[tex]\angle A=7\times 5= 35\°\\\angle B=18\times 5= 90\°\\\angle C=11\times 5= 55\°[/tex]
Therefore the measure of the angles of a right angled triangle ABC are,
[tex]\angle A=35\°\\\angle B= 90\°\\\angle C= 55\°[/tex]
