Studdy AI Logo
Math  /  Geometry

QuestionFind the measures of the interior angles of the triangle ∠A=\angle A= ∘{ }^{\circ} □\square ∠B=\angle B= □\square ∠C=□∘\angle C=\square^{\circ}

Studdy Solution

STEP 1

1. We are given a triangle △ABC \triangle ABC .
2. The measures of the angles are ∠A=48∘ \angle A = 48^\circ , ∠B=x∘ \angle B = x^\circ , and ∠C=(x−44)∘ \angle C = (x - 44)^\circ .
3. The sum of the interior angles of a triangle is 180∘ 180^\circ .

STEP 2

1. Set up an equation using the sum of the interior angles of the triangle.
2. Solve the equation for x x .
3. Substitute the value of x x back into the expressions for ∠B \angle B and ∠C \angle C to find their measures.

STEP 3

Set up the equation using the sum of the interior angles of a triangle:
∠A+∠B+∠C=180∘ \angle A + \angle B + \angle C = 180^\circ
Substitute the given values:
48∘+x∘+(x−44)∘=180∘ 48^\circ + x^\circ + (x - 44)^\circ = 180^\circ

STEP 4

Simplify the equation:
48+x+x−44=180 48 + x + x - 44 = 180
Combine like terms:
2x+4=180 2x + 4 = 180

STEP 5

Solve for x x :
Subtract 4 from both sides:
2x=176 2x = 176
Divide both sides by 2:
x=88 x = 88

STEP 6

Substitute x=88 x = 88 back into the expressions for ∠B \angle B and ∠C \angle C :
∠B=x=88∘ \angle B = x = 88^\circ
∠C=x−44=88−44=44∘ \angle C = x - 44 = 88 - 44 = 44^\circ
The measures of the interior angles of the triangle are:
∠A=48∘ \angle A = 48^\circ ∠B=88∘ \angle B = 88^\circ ∠C=44∘ \angle C = 44^\circ

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord