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A and B are complementary angles. If m_A = (6x + 29) and m

B = (x + 5)', then find the measure of A.

User Uvsmtid
by
8.8k points

2 Answers

9 votes

Answer:

The measurement of angle A is: 77°

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\\(7x)/(7) = (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°

User Mrcendre
by
8.1k points
3 votes

Answer:

m∠
A=77°

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)


(7x)/(7)=(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!

User Mic Fok
by
8.1k points
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