Question

1. in the diagram shown, qw and sy intersect at point r and kj by dotted - lines. (a) name a linear pair of angles from the diagram. (b) name a pair of vertical angles from the diagram. (c) if m∠krw = m∠qrj, then find the measure of ∠krw and the measure of ∠qrj. 7. in a linear angle pair, the measure of the larger angle is 15 degrees less than twice the measure of the smaller angle. find the measures of both angles. show the work that leads to your answers. 8. lines r and s intersect as shown in the diagram below. find the value of x algebraically. justify your approach. (10x - 20) 8(x + 1) 10x - 20 8(x + 1) reasoning 9. two lines, j and k, intersect to form four angles, one of which is a right angle as marked. explain why each of the other four angles must also be right angles. 3 2 1 n - gen math geometry - unit 1 - beginning concepts - lesson 6 emathinstruction, red hook, ny 12571, © 2023

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. So, \(10x - 20=8(x + 1)\)

Step2: Expand the right - hand side

Expand \(8(x + 1)\) to get \(8x+8\). The equation becomes \(10x - 20=8x + 8\)

Step3: Move \(x\) terms to one side

Subtract \(8x\) from both sides: \(10x-8x - 20=8x-8x + 8\), which simplifies to \(2x-20 = 8\)

Step4: Isolate \(x\)

Add 20 to both sides: \(2x-20 + 20=8 + 20\), getting \(2x=28\). Then divide both sides by 2: \(x = 14\)

Answer:

\(x = 14\)