Answer:
The Value of x= 7.
m∠A= 21°
m∠B= 80°
m∠C= 79°
Step-by-step explanation:
Given:
m∠A = 2x+7
m∠B = 10x+10
m∠C = 8x+23
We need to find the value of x and measures of each angle.
Now by angle sum property which states that sum of all angles of a triangle are 180°.
Hence from above statement we can say in ΔABC;
m∠A+m∠B+m∠C=180
Now substituting the given values in above equation we get;
[tex]2x+7+10x+10+8x+23=180\\2x+10x+8x+7+10+23=180\\20x+40=180\\20x=180-40\\20x=140\\\\x=\frac{140}{20} =7[/tex]
Hence value of x is 7.
Substituting the value of x in all angles we get;
m∠A=[tex]2x+7=2\times7+7=14+7=21\°[/tex]
m∠B=[tex]10x+10=10\times7+10=70+10=80\°[/tex]
m∠C=[tex]8x+23= 8\times7 +23 = 56+23=79\°[/tex]
