Question

∠A and ∠B are complementary angles. If ∠A = (7+4x)° and ∠B= ( x+23 ) , then which is a true statement.
a. ∠A is acute
b. ∠A and ∠B are 45° each
c. ∠A is obtuse
d. ∠B > ∠A

Answer 1

Step-by-step explanation:

angle A + angle B = 180°.

(7+4x) + (X+23) = 180°

7 + 4x + X + 23 = 180°.

5x + 30 = 180°.

5x = 180° - 30.

5x = 150°.

X = 150°/5.

X = 30°.

Answer 2

a. ∠A is acute

Given:

Two complementary angles ∠A = (7+4x)° and ∠B= ( x+23 )

Solution:

As we know that the sum of complementary angles is 90°

So,

(7+4x)° + ( x+23 )° = 90

30 + 5x = 90

5x = 60

x = 60/5

x = 12

so ∠A = 7 + 4 (12) = 7 + 48 = 55°

     ∠B = ( 12 + 23 ) = 35°

Hence ∠A  is acute angle.