Question

Angles of measure (a + 5)degree and (4a – 15)degree
are complementary. What is the measure of each
angle ?

Answer 1

Answer:

The two angles are 25° and 65°.

Step-by-step explanation:

We know that complementary means the sum of two adjacent angles is 90°.

So,

(a+5)+(4a-15)=90°

5a-10=90°

5a=100°

a=20°

Therefore the measure of two angles will be (20°+5)=25° and (4(20°)-15)=65°.

Hope my answer helps you my friend..Please make me the brainliest if my answer is correct..

Answer 2

Given: 1st angle$=\[{\left( {a + 5} \right)^ \circ }\]$, 2nd angle$=\[{\left( {4a - 15} \right)^ \circ }\]$

To find: the measure of each given angle.

Solution:

Know that from the question, the given angles are complementary, i.e., sum if both the angles is 45 degrees.

Form the equation according to the conditions given in the question, to find the value of x.

$\[\begin{array}{l}{\left( {a + 5} \right)^ \circ } + {\left( {4a - 15} \right)^ \circ } = {90^ \circ }\\ \Rightarrow 4a + a - 15 + 5 = 90\\ \Rightarrow 5x - 10 = 90\\ \Rightarrow 5x = 90 - 10\end{array}\]$

$\[\begin{array}{l} \Rightarrow 5x = 80\\ \Rightarrow x = \frac{{80}}{5}\\ \Rightarrow x = {16^ \circ }\end{array}\]$

Find the measure of 1st angle.

$\[\begin{array}{l}{\left( {a + 5} \right)^ \circ } = {\left( {16 + 5} \right)^ \circ }\\ \Rightarrow {\left( {a + 5} \right)^ \circ } = {21^ \circ }\end{array}\]$

Find the measure of 2nd angle.

$\[\begin{array}{l}{\left( {4a - 15} \right)^ \circ } = {\left( {4 \times 16 - 15} \right)^ \circ }\\ \Rightarrow {\left( {4a - 15} \right)^ \circ } = {\left( {64 - 15} \right)^ \circ }\\ \Rightarrow {\left( {4a - 15} \right)^ \circ } = {49^ \circ }\end{array}\]$

Hence, the measure of both angles are $\[{21^ \circ },{49^ \circ }\]$ respectively.