The angles of the triangle in the diagram are \((x+30)^\circ\), \(2x^\circ\) and \((3x-18)^\circ\). (a) Form an equation in \(x\) and solve it. [2] (b) Find...
Question 1 Report
The angles of the triangle in the diagram are \((x+30)^\circ\), \(2x^\circ\) and \((3x-18)^\circ\).
(a) Form an equation in \(x\) and solve it. [2]
(b) Find the size of the largest angle of the triangle. [2]
Answer Details
The angles inside any triangle add up to \(180^\circ\). That fact converts the three algebraic angles into a single equation.
(a) Adding the three expressions:
\[(x+30)+2x+(3x-18)=180\]
Collecting like terms gives \(6x+12=180\) [M1]. Subtracting \(12\) gives \(6x=168\), so
\[x=28\]
scoring the accuracy mark [A1].
(b) Substitute \(x=28\) into each expression to find the actual angles:
| Expression | Value |
|---|---|
| \((x+30)^\circ\) | \(58^\circ\) |
| \(2x^\circ\) | \(56^\circ\) |
| \((3x-18)^\circ\) | \(66^\circ\) |
Working out all three angles earns the method mark [M1], and the largest of them is \(66^\circ\) [A1]. The three values total \(58+56+66=180^\circ\), confirming the work.
You cannot tell which expression gives the largest angle just by looking at it, since \(3x-18\) beats \(2x\) only because \(x\) happens to be \(28\). Always evaluate all three, then compare.
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