Parallel Lines Angles E6A5Fe

Question: Reasoning in geometry Topic 3: Parallel lines and angles QUESTION 1 Find $x$, giving reasons. a $x^\circ$ $70^\circ$ position_hint: top-left; graph: two parallel horizontal lines cut by one rising transversal, with $x^\circ$ at the upper intersection below the top line and left of the transversal, and $70^\circ$ at the lower intersection above the bottom line and right of the transversal. b $x^\circ$ $120^\circ$ position_hint: top-center; graph: two slanted parallel lines cut by a horizontal transversal, with $x^\circ$ at the left intersection above the transversal and $120^\circ$ at the right intersection below the transversal. c $x^\circ$ $110^\circ$ position_hint: top-right; graph: two slanted parallel lines cut by a horizontal transversal, with $x^\circ$ at the left intersection below the transversal and $110^\circ$ at the right intersection below the transversal. QUESTION 2 Find the value of the pronumeral, giving reasons. a y^\circ x^\circ $100^\circ$ position_hint: top-left; graph: two parallel horizontal lines cut by a rising transversal, with $y^\circ$ above the top line on the right, $x^\circ$ below the top line on the right, and $100^\circ$ above the bottom line on the left. b y^\circ x^\circ $75^\circ$ position_hint: top-center; graph: two parallel horizontal lines cut by a rising transversal, with $y^\circ$ above the top line on the left, $x^\circ$ above the top line on the right, and $75^\circ$ above the bottom line on the right. c $110^\circ$ x^\circ y^\circ position_hint: top-right; graph: two parallel horizontal lines cut by a rising transversal, with $110^\circ$ below the top line on the right, $x^\circ$ above the bottom line on the right, and $y^\circ$ below the bottom line on the left. d y^\circ x^\circ $45^\circ$ position_hint: center-left; graph: two parallel horizontal lines cut by a rising transversal, with $y^\circ$ below the top line on the left, $x^\circ$ below the top line on the right, and $45^\circ$ above the bottom line on the right. e y^\circ x^\circ $115^\circ$ position_hint: center; graph: two parallel horizontal lines cut by a rising transversal, with $y^\circ$ above the top line on the left, $x^\circ$ below the top line on the right, and $115^\circ$ above the bottom line on the left. f y^\circ x^\circ $70^\circ$ position_hint: center-right; graph: three parallel horizontal lines cut by a rising transversal, with $y^\circ$ below the top line on the left, $x^\circ$ below the top line on the right, and $70^\circ$ above the bottom line on the right. QUESTION 3 Find the value of the pronumeral, giving reasons. a $x^\circ$ $108^\circ$ position_hint: lower-left; graph: two parallel slanted vertical lines standing on a horizontal base, with $x^\circ$ at the left bottom interior angle and $108^\circ$ at the right bottom interior angle. b $b^\circ$ $a^\circ$ $40^\circ$ position_hint: lower-center; graph: a horizontal line with a vertical line at center and a slanted line on each side marked parallel, with $b^\circ$ between the left slanted line and vertical, $a^\circ$ at the top of the vertical between it and the right slanted line, and $40^\circ$ at the lower right between the right slanted line and the baseline. c $c^\circ$ $b^\circ$ $50^\circ$ $a^\circ$ $a^\circ$ position_hint: lower-right; graph of a triangle between two parallel horizontal lines, with apex on the top line, $50^\circ$ inside the triangle near the apex, $c^\circ$ above-left of the apex on the top line, $b^\circ$ above-right of the apex on the top line, and $a^\circ$ at both base angles. d $30^\circ$ x^\circ $60^\circ$ position_hint: lower-left; graph of two parallel horizontal lines with a broken transversal between them, $30^\circ$ at the upper intersection, $x^\circ$ at the middle kink, and $60^\circ$ at the lower intersection. e $80^\circ$ x^\circ position_hint: lower-center; graph of two vertical parallel lines and two horizontal segments forming a U-shape, with $80^\circ$ at the lower-left corner and $x^\circ$ at the upper-right corner. f $50^\circ$ $a^\circ$ $40^\circ$ position_hint: lower-right; graph of several rays meeting at a vertex, with $50^\circ$ between the left slanted ray and the middle rising ray, $a^\circ$ at the vertex between the left slanted ray and the lower-right ray, and $40^\circ$ between the right rising ray and the lower-right ray. Question 1 a $x^\circ = 50^\circ$ Question 1 b $m^\circ = 110^\circ$ Question 1 c $x^\circ = 50^\circ$ $y^\circ = 130^\circ$ Question 1 d $x^\circ = 120^\circ$ Question 1 e $x^\circ = 70^\circ$ Question 1 f $x^\circ = 40^\circ$ Question 2 a $x^\circ = 120^\circ$ Question 2 b $a^\circ = 25^\circ$ Question 2 c $x^\circ = 30^\circ$ Question 2 d $y^\circ = 55^\circ$ Question 2 e $a^\circ = 30^\circ$ Question 2 f $a^\circ = 95^\circ$ $b^\circ = 95^\circ$ $c^\circ = 85^\circ$ Question 3 a $x^\circ = 60^\circ$ Question 3 b $x^\circ = 80^\circ$ $y^\circ = 35^\circ$ Question 3 c $x^\circ = 90^\circ$ Graph shape position_hint=top-left: intersecting lines forming vertical opposite angles, with one angle marked $50^\circ$ and adjacent angles labeled $x^\circ$ and $y^\circ$.