Question

∠1 and, ∠2 are supplementary angles. If m ∠ 1 = (7x + 18) ∘ m∠1=(7x+18) ∘and m ∠ 2 = (x + 18) ∘ m∠2=(x+18)∘ , then find the measure of angle, ∠1.

Answer 1

m∠1 = 144°

Explanation:

Step 1: Find the value of x:

Since angles 1 and 2 are supplementary, the sum of their measures equals 180°:

∠1 + ∠2 = 180

Thus, we can find x by substituting 7x + 18 for ∠1 and x + 18 for ∠2 in the equation above:

7x + 18 + x + 18 = 180

(8x + 36 = 180) - 36

(8x = 144) / 8

x = 18

Thus, x = 18.

Step 2: Find the measure of angle 1:

Now we can find the measure of angle 1 by substituting 18 for x in 7x + 18:

m∠1 = 7(18) + 18

m∠1 = 126 + 18

m∠1 = 144

Thus, the measure of angle 1 is 144°.