Answer:
The measure of angle b is 35°.
Step-by-step explanation:
Given:
the measure of angle a is 15 less than twice the measure of angle b
So we can say that;
[tex]a=2b-15[/tex]
Also Given:
measure of angle c equals the sum of the measures of angle a and angle b
So we can say that;
[tex]c=a+b[/tex]
But [tex]a=2b-15[/tex]
So we can say that
[tex]c=2b-15+b = 3b-15[/tex]
we need to find the measure of angle b.
Solution:
In Δ abc,
Sum of measures of all angles of triangle is 180°.
So we can say that;
[tex]a+b+c=180[/tex]
Substituting the value of a and c in above equation we get;
[tex]2b-15+b+3b-15=180\\\\6b-30=180[/tex]
Adding both side by 30 we get;
[tex]6b-30+30=180+30\\\\6b=210[/tex]
Dividing both side by 6 we get;
[tex]\frac{6b}{6}=\frac{210}{6}\\\\b=35[/tex]
Hence the measure of angle b is 35°.
