Question

solve using two linear equations in two variables and cramers rule. one acute angle of a right triangle is 7° larger than twice the other acute angle. what are the measures of the acute angles? the acute angles are □°. (type an integer or a fraction. use a comma to separate answers as needed.)

Explanation:

Step1: Define variables

Let the two acute angles be $x$ and $y$.

Step2: Set up equations

Sum of acute angles: $x + y = 90$
Given relation: $x = 2y + 7$

Step3: Write in standard form

Equation1: $x + y = 90$
Equation2: $x - 2y = 7$

Step4: Calculate determinant $D$

$$D =
LATEXBLOCK0
= (1)(-2) - (1)(1) = -3$$

Step5: Calculate $D_x$

$$D_x =
LATEXBLOCK1
= (90)(-2) - (1)(7) = -187$$

Step6: Calculate $D_y$

$$D_y =
LATEXBLOCK2
= (1)(7) - (90)(1) = -83$$

Step7: Find $x$ and $y$

$x = \frac{D_x}{D} = \frac{-187}{-3} = \frac{187}{3}$
$y = \frac{D_y}{D} = \frac{-83}{-3} = \frac{83}{3}$

Answer:

$\frac{83}{3}, \frac{187}{3}$