Question

The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles.

Answer 1

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 2

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:

$\begin{array}{lrcll}(1) & y & = & 2x - 15\\(2)& x + y & =&90\\(3)& x + 2x - 15 & =&90&\text{Substituted (1) into (2)}\\& 3x- 15 & = & 90&\text{Simplified}\\&3x & = & 105&\text{Added 15 to each side}\\ (4)& x & = & \mathbf{35}&\text{Divided each side by 3}\\& y & = & 2(35) - 15&\text{Substituted (4) into (1)}\\& & = & 70 - 15&\text{Simplified}\\&&=&\mathbf{55}&\end{array}$

x = 35°; y = 55°

Check:

$\begin{array}{ccc}55 = 2(35) - 15 & \qquad & 35 + 55 = 90\\55 = 70 - 15 & \qquad & 90 = 90\\55 = 55 && \\\end{array}$

It checks.