Question

4 fill in the blank 1 point find the values of x and the missing angle measurement. (pictures may not be to scale) (x + 16)° (4x - 5)° x = type your answer...°, ∠a = type your answer...° and ∠b = type your answer...°

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(x + 16=4x - 5\).

Step2: Solve for \(x\)

Subtract \(x\) from both sides: \(16 = 3x-5\).
Add \(5\) to both sides: \(21 = 3x\).
Divide by \(3\): \(x = 7\).

Step3: Find \(\angle A\)

Substitute \(x = 7\) into \(x + 16\): \(\angle A=7 + 16=23^{\circ}\).

Step4: Find \(\angle B\)

Since \(\angle A\) and \(\angle B\) are supplementary (they form a linear pair), \(\angle B = 180-\angle A\).
So, \(\angle B=180 - 23=157^{\circ}\).

Answer:

\(x = 7\), \(\angle A = 23\), \(\angle B = 157\)