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QuestionIn a triangle, if m∠A=(x−2)∘m \angle A=(x-2)^{\circ}, m∠B=(x−2)∘m \angle B=(x-2)^{\circ}, and m∠C=(3x+4)∘m \angle C=(3x+4)^{\circ}, find each angle's measure.

Studdy Solution

STEP 1

Assumptions1. The measure of angle A is (x−)∘(x-)^\circ . The measure of angle B is (x−)∘(x-)^\circ
3. The measure of angle C is (3x+4)∘(3x+4)^\circ
4. The sum of the measures of the angles in a triangle is 180∘180^\circ

STEP 2

We can form an equation using the fact that the sum of the measures of the angles in a triangle is 180∘180^\circ.
m∠A+m∠B+m∠C=180∘m \angle A + m \angle B + m \angle C =180^\circ

STEP 3

Substitute the given expressions for the measures of the angles into the equation.
(x−2)∘+(x−2)∘+(3x+)∘=180∘(x-2)^\circ + (x-2)^\circ + (3x+)^\circ =180^\circ

STEP 4

implify the equation by removing the degree symbol and combining like terms.
2x−4+3x+4=1802x -4 +3x +4 =180

STEP 5

Further simplify the equation.
5x=1805x =180

STEP 6

olve the equation for xx by dividing both sides by5.
x=1805x = \frac{180}{5}

STEP 7

Calculate the value of xx.
x=36x =36

STEP 8

Now that we have the value of xx, we can substitute it back into the expressions for the measures of the angles to find their degree measures.
For m∠Am \angle A and m∠Bm \angle B(x−2)∘=(36−2)∘(x-2)^\circ = (36-2)^\circFor m∠Cm \angle C(3x+4)∘=(3∗36+4)∘(3x+4)^\circ = (3*36+4)^\circ

STEP 9

Calculate the degree measures of the angles.
For m∠Am \angle A and m∠Bm \angle B(36−2)∘=34∘(36-2)^\circ =34^\circFor m∠Cm \angle C(3∗36+4)∘=112∘(3*36+4)^\circ =112^\circThe degree measures of the angles in the triangle arem∠A=34∘m∠B=34∘m∠C=112∘\begin{array}{l} m \angle A=34^{\circ} \\ m \angle B=34^{\circ} \\ m \angle C=112^{\circ} \end{array}

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