Question

A and B are complementary angles. If m_A = (6x + 29) and m
B = (x + 5)', then find the measure of A.

Answer 1

Answer:

m∠$A=77$°

Step-by-step explanation:

Complementary angles are a pair of angles whose measures have a sum of $90$°. Since m∠$A$ = $6x+29$ and m∠$B$ = $x+5$, we can write the following equation to solve for $x$:

$6x+29+x+5=90$

Solving for $x$, we get:

$6x+29+x+5=90$

$7x+34=90$ (Simplify LHS)

$7x+34-34=90-34$ (Subtract $34$ from both sides of the equation to isolate $x$)

$7x=56$ (Simplify)

$\frac{7x}{7}=\frac{56}{7}$ (Divide both sides of the equation by $7$ to get rid of $x$'s coefficient)

$x=8$

Therefore, m∠$A=6x+29=6(8)+29=48+29=77$°. Hope this helps!

Answer 2

Answer:

The measurement of angle A is: 77°

Step-by-step explanation:

First of all, let us define complementary angles

The angles whose sum is 90° are called complementary angles.

Given angles are:

m∠A = 6x+29

m∠B = x+5

With respect to the definition, the sum of both angles will be 90°

Writing this mathematically we get

$A+B = 90\\6x+29+x+5 = 90\\7x+34=90\\7x = 90-34\\7x = 56\\\frac{7x}{7} = \frac{56}{7}\\x = 8$

Putting the value of x in the expression for angle A

$A = 6x+ 29 = 6(8)+29 =48+29\\A = 77$

Hence,

The measurement of angle A is: 77°