Question 396·Easy·Math

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In right triangle $\triangle ABC$ , $\angle C$ is the right angle. If the measure of $\angle A$ is $35^\circ$ , what is the measure of $\angle B$ ?

In a right triangle, one angle is $90^\circ$ , so the other two angles add to $90^\circ$ . Subtract the given non-right angle from that total to find the missing one. Don't split the $90^\circ$ equally: equal angles need an additional clue, and this takes only one subtraction, so Desmos isn't needed.

Hints

Hint 1
A right angle measures $90^\circ$ . Since a triangle’s angles total $180^\circ$ , how much is left for the other two angles together?
Hint 2
The two non-right angles share what’s left, but they don’t have to share it equally. Subtract the given angle from their total to find the angle at $B$ .

Step-by-step

Use the right-triangle angle sum
Step 1
Find the total for the two non-right angles
No Desmos needed. This angle fact leaves only one subtraction. A right angle measures $90^\circ$ . A triangle’s angles add to $180^\circ$ , so the other two angles add to $90^\circ$ . Here $m\angle A$ means the measure of angle $A$ :
$m\angle A+m\angle B=90^\circ.$
Step 2
Put the given angle into the equation
The problem gives $m\angle A=35^\circ$ , so replace $m\angle A$ with $35^\circ$ :
$35^\circ+m\angle B=90^\circ.$
Step 3
Find the angle at B
Subtract $35^\circ$ from both sides:
$\begin{aligned}m\angle B&=90^\circ-35^\circ\m\angle B&=55^\circ.\end{aligned}$
So $\angle B$ measures $55^\circ$ . Choice C.

Lessons that teach this

SAT Geometry and TrigonometryIntermediateCoreUse triangle angle theorems

Question 396·Easy·Math

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