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Take Note: The sum of the angles inside a triangle is always $\boldsymbol{180}^\circ$. First triangle: $\angle x^\circ + \boldsymbol{75}^\circ + \boldsymbol{35}^\circ = 180^\circ$…

Category: geometry Updated: 2026-02-09

Question

take note: the sum of the angles inside a triangle is always $\boldsymbol{square}^{circ}$.find the missing angles of the following triangles:$angle x^{circ}+\boldsymbol{square}^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ plug in what is given.$angle x^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ add the given angles.$angle x^{circ}=\boldsymbol{square}^{circ}$ subtract from $180^{circ}$$angle x^{circ}+\boldsymbol{square}^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ plug in what is given.$angle x^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ add the given angles.$angle x^{circ}=\boldsymbol{square}^{circ}$ subtract from $180^{circ}$

Solution Steps

  1. Understand the question

    take note: the sum of the angles inside a triangle is always $\boldsymbol{square}^{circ}$.find the missing angles of the following triangles:$angle x^{circ}+\boldsymbol{square}^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ plug in what is given.$angle x^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ add the given angles.$angle x^{circ}=\boldsymbol{square}^{circ}$ subtract from $180^{circ}$$angle x^{circ}+\boldsymbol{square}^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ plug in what is given.$angle x^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ add the given angles.$angle x^{circ}=\boldsymbol{square}^{circ}$ subtract from $180^{circ}$

  2. Explanation

    Step1: Plug in given angles

    $\angle x^\circ + 75^\circ + 35^\circ = 180^\circ$

    Step2: Add known angles

    $\angle x^\circ + 110^\circ = 180^\circ$

    Step3: Solve for first $\angle x$

    $\angle x^\circ = 180^\circ - 110^\circ = 70^\circ$

    Step4: Plug in second triangle angles

    $\angle x^\circ + 50^\circ + 100^\circ = 180^\circ$

    Step5: Add known angles

    $\angle x^\circ + 150^\circ = 180^\circ$

    Step6: Solve for second $\angle x$

    $\angle x^\circ = 180^\circ - 150^\circ = 30^\circ$

    Step7: Fill top note

    Sum of triangle angles = $180^\circ$

  3. Final answer

    Take Note: The sum of the angles inside a triangle is always $\boldsymbol{180}^\circ$.

    First triangle:
    $\angle x^\circ + \boldsymbol{75}^\circ + \boldsymbol{35}^\circ = 180^\circ$
    $\angle x^\circ + \boldsymbol{110}^\circ = 180^\circ$
    $\angle x^\circ = \boldsymbol{70}^\circ$

    Second triangle:
    $\angle x^\circ + \boldsymbol{50}^\circ + \boldsymbol{100}^\circ = 180^\circ$
    $\angle x^\circ + \boldsymbol{150}^\circ = 180^\circ$
    $\angle x^\circ = \boldsymbol{30}^\circ$

Answer

Explanation

Step1: Plug in given angles

$\angle x^\circ + 75^\circ + 35^\circ = 180^\circ$

Step2: Add known angles

$\angle x^\circ + 110^\circ = 180^\circ$

Step3: Solve for first $\angle x$

$\angle x^\circ = 180^\circ - 110^\circ = 70^\circ$

Step4: Plug in second triangle angles

$\angle x^\circ + 50^\circ + 100^\circ = 180^\circ$

Step5: Add known angles

$\angle x^\circ + 150^\circ = 180^\circ$

Step6: Solve for second $\angle x$

$\angle x^\circ = 180^\circ - 150^\circ = 30^\circ$

Step7: Fill top note

Sum of triangle angles = $180^\circ$

Answer

Take Note: The sum of the angles inside a triangle is always $\boldsymbol{180}^\circ$.

First triangle:
$\angle x^\circ + \boldsymbol{75}^\circ + \boldsymbol{35}^\circ = 180^\circ$
$\angle x^\circ + \boldsymbol{110}^\circ = 180^\circ$
$\angle x^\circ = \boldsymbol{70}^\circ$

Second triangle:
$\angle x^\circ + \boldsymbol{50}^\circ + \boldsymbol{100}^\circ = 180^\circ$
$\angle x^\circ + \boldsymbol{150}^\circ = 180^\circ$
$\angle x^\circ = \boldsymbol{30}^\circ$

Question Image

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Question Analysis

Subject mathematics
Sub Subject geometry
Education Level middle school
Difficulty unspecified
Question Type with image, calculation
Multi Question No
Question Count 1
Analysis Status completed
Analyzed At 2026-02-09T20:19:57

OCR Text

Show OCR extraction
take note: the sum of the angles inside a triangle is always $\boldsymbol{square}^{circ}$.find the missing angles of the following triangles:$angle x^{circ}+\boldsymbol{square}^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ plug in what is given.$angle x^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ add the given angles.$angle x^{circ}=\boldsymbol{square}^{circ}$ subtract from $180^{circ}$$angle x^{circ}+\boldsymbol{square}^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ plug in what is given.$angle x^{circ}+\boldsymbol{square}^{circ}=180^{circ}$ add the given angles.$angle x^{circ}=\boldsymbol{square}^{circ}$ subtract from $180^{circ}$

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mathematicsgeometrywith image, calculationmiddle schoolturns-1

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