Answer:
A= 35°
b= 55°
Step-by-step explanation:
Let's take the small angles of the right angle triangle to be and b
a+b +90= 180....(sum of angles in a right angle triangle)
The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle
2a-15= b
a+2a -15 +90= 180
3a = 180-75
3a= 105
a= 105/3
a= 35°
a+b +90= 180.
35+b+90= 180
b = 180-90-35
b = 55°
Answer:
x = 35°; y = 55°
Step-by-step explanation:
Let x = one of the angles
and y = the other angle. Then
2x = twice the measure of x and
2x - 15 = 15 less than twice the measure of x
You have two conditions
(1) y = 2x - 15
(2) x+ y = 90
Calculations:
[tex]\begin{array}{lrcll}(1) & y & = & 2x - 15\\(2)& x + y & =&90\\(3)& x + 2x - 15 & =&90&\text{Substituted (1) into (2)}\\& 3x- 15 & = & 90&\text{Simplified}\\&3x & = & 105&\text{Added 15 to each side}\\ (4)& x & = & \mathbf{35}&\text{Divided each side by 3}\\& y & = & 2(35) - 15&\text{Substituted (4) into (1)}\\& & = & 70 - 15&\text{Simplified}\\&&=&\mathbf{55}&\end{array}\\[/tex]
x = 35°; y = 55°
Check:
[tex]\begin{array}{ccc}55 = 2(35) - 15 & \qquad & 35 + 55 = 90\\55 = 70 - 15 & \qquad & 90 = 90\\55 = 55 && \\\end{array}[/tex]
It checks.
