A site engineer fixes two steel braces so that they meet the ground at the same point and lie along a straight guide line marked on the concrete. The angle ...
Question 1 Report
A site engineer fixes two steel braces so that they meet the ground at the same point and lie along a straight guide line marked on the concrete. The angle between the first brace and the line is \(4x - 8\) degrees, and the angle between the second brace and the line is \(2x + 14\) degrees.
- Form and solve an equation to find the value of \(x\). (3)
- Find the size of the smaller angle. (1)
Answer Details
This question tests forming and solving an equation from the angles-on-a-straight-line fact.
(a) The two braces meet the guide line at the same point, on the same side, so the two marked angles together make up the straight angle along the guide line. Angles on a straight line sum to \(180^\circ\), giving the equation:
\[(4x-8) + (2x+14) = 180\]Simplifying:
\[6x + 6 = 180\] \[6x = 174\] \[x = 29\][3] (forming the equation, simplifying, and solving for \(x\))
(b) Substituting \(x=29\) into each expression: \(4(29)-8 = 108^\circ\) and \(2(29)+14 = 72^\circ\). The smaller angle is \(72^\circ\). [1]
Check: \(108 + 72 = 180^\circ\), confirming the two angles do lie on a straight line as required.
When an equation gives an unknown like \(x\), always substitute back into both original expressions (not just one) so you can compare them and correctly identify which is the smaller angle, rather than assuming the algebraically simpler expression is smaller.
Download The App On Google Playstore
Everything you need to excel in your exams
