Question 316·Medium·Math

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In $\triangle GHI$ , the measures of $\angle G$ and $\angle H$ are $k^\circ$ and $(k+40)^\circ$ , respectively. The measure of $\angle I$ is $50^\circ$ . What is the value of $k$ ? (Disregard the degree symbol when entering your answer.)

Your answer

A triangle angle sum question gives three angle measures in one triangle, sometimes using the same variable more than once. Add all three angle expressions and set their total to $180^\circ$ . Keep each copy of the variable when you translate the angles. Use a Desmos regression to find the variable, then check whether the question asks for that variable or an angle.

Hints

Hint 1
The interior-angle sum says the three angles inside a triangle add to $180^\circ$ . What expression represents the total of the angles at $G$ , $H$ , and $I$ ?
Hint 2
Angle $H$ is $k+40$ , not $40$ . The extra $40$ belongs to that angle, while angle $G$ still contributes its own $k$ . Which equation makes their total $180$ ?

Step-by-step

Add the triangle’s angles
Step 1
Write the angle-sum equation
The interior angles, the angles inside a triangle, add to $180^\circ$ . Angle $G$ contributes $k$ , angle $H$ contributes $k+40$ , and angle $I$ contributes $50$ , so write:
$k+(k+40)+50=180.$
Keep both $k$ terms: angle $H$ is $40^\circ$ more than angle $G$ , but angle $G$ still counts.
Step 2
Find the value of the variable
Type $k+(k+40)+50\sim180$ into Desmos. The $\sim$ makes a regression: Desmos finds the value of $k$ that makes the two sides match. Under PARAMETERS, it shows $k=45$ . Enter $k$ itself, not the measure $k+40$ of angle $H$ . The value of $k$ is $45$ . Grid in 45.

Lessons that teach this

SAT Geometry and TrigonometryIntermediateCoreUse triangle angle theorems

Question 316·Medium·Math

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