Angles at a point and on a line questions with answers

Questions

1. Question 1Angles on a straight line

   In the diagram, $AOB$ is a straight line. Find $x$.

   Show the worked solution

   1. Step 1: Add up the angles along the line AOB$x^\circ + 44^\circ + 104^\circ = 180^\circ$
   2. Step 2: Find x$x = 180 - 44 - 104$$x = 32$ (∠s on a str. line)
2. Question 2Angles at a point

   In the diagram, the line segments $OA$, $OB$ and $OC$ meet at the point $O$. Find $x$.

   Show the worked solution

   1. Step 1: Add up the angles round the point O$129^\circ + x^\circ + 93^\circ = 360^\circ$
   2. Step 2: Find x$x = 360 - 129 - 93$$x = 138$ (∠s at a pt.)
3. Question 3Vertically opposite angles

   In the diagram, the straight lines $AB$ and $CD$ meet at $O$. $OE$ is a straight line between $OA$ and $OC$. Find $x$.

   Show the worked solution

   1. Step 1: ∠AOC is made of two parts$\angle AOC = 41^\circ + 45^\circ$$\angle AOC = 86^\circ$
   2. Step 2: Find x and give the reason$x = 86$ (vert. opp. ∠s)
4. Question 4Complementary and supplementary angles

   $\angle ABC$ and $\angle PQR$ are supplementary angles. Find $x$.

   Show the worked solution

   1. Step 1: Supplementary angles: what do they add up to?$x^\circ + 92^\circ = 180^\circ$
   2. Step 2: Find x$x = 180 - 92$$x = 88$ (supplementary ∠s)
5. Question 5Angles as expressions: on a line or at a point

   In the diagram, $AOB$ is a straight line. Find $x$.

   Show the worked solution

   1. Step 1: Write an equation in x$(2x + 20)^\circ + (3x + 15)^\circ = 180^\circ$ (∠s on a str. line)
   2. Step 2: Collect like terms and solve$5x + 35 = 180$$5x = 145$$x = 29$
6. Question 6Vertically opposite expressions

   In the diagram, the straight lines $AB$ and $CD$ meet at $O$. Find $x$.

   Show the worked solution

   1. Step 1: Write an equation in x$5x - 20 = 2x + 25$ (vert. opp. ∠s)
   2. Step 2: Collect the x terms on one side and the numbers on the other$5x - 2x = 25 + 20$$3x = 45$$x = 15$