At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Which set of three angles could represent the interior angles of a triangle?

A. [tex]\( 26^{\circ}, 51^{\circ}, 103^{\circ} \)[/tex]
B. [tex]\( 29^{\circ}, 54^{\circ}, 107^{\circ} \)[/tex]
C. [tex]\( 35^{\circ}, 35^{\circ}, 20^{\circ} \)[/tex]
D. [tex]\( 10^{\circ}, 90^{\circ}, 90^{\circ} \)[/tex]


Sagot :

To determine which set of three angles can represent the interior angles of a triangle, we need to know that the sum of the interior angles of any triangle must be [tex]\(180^\circ\)[/tex]. We will calculate the sum for each set of angles provided and check which one sums to [tex]\(180^\circ\)[/tex].

First set of angles: [tex]\(26^\circ\)[/tex], [tex]\(51^\circ\)[/tex], [tex]\(103^\circ\)[/tex]
[tex]\[ 26^\circ + 51^\circ + 103^\circ = 180^\circ \][/tex]
This set sums to [tex]\(180^\circ\)[/tex], so it could represent the interior angles of a triangle.

Second set of angles: [tex]\(29^\circ\)[/tex], [tex]\(54^\circ\)[/tex], [tex]\(107^\circ\)[/tex]
[tex]\[ 29^\circ + 54^\circ + 107^\circ = 190^\circ \][/tex]
This set sums to [tex]\(190^\circ\)[/tex], which is more than [tex]\(180^\circ\)[/tex], so it does not represent the interior angles of a triangle.

Third set of angles: [tex]\(35^\circ\)[/tex], [tex]\(35^\circ\)[/tex], [tex]\(20^\circ\)[/tex]
[tex]\[ 35^\circ + 35^\circ + 20^\circ = 90^\circ \][/tex]
This set sums to [tex]\(90^\circ\)[/tex], which is less than [tex]\(180^\circ\)[/tex], so it does not represent the interior angles of a triangle.

Fourth set of angles: [tex]\(10^\circ\)[/tex], [tex]\(90^\circ\)[/tex], [tex]\(90^\circ\)[/tex]
[tex]\[ 10^\circ + 90^\circ + 90^\circ = 190^\circ \][/tex]
This set sums to [tex]\(190^\circ\)[/tex], which is more than [tex]\(180^\circ\)[/tex], so it does not represent the interior angles of a triangle.

Since only the first set of angles sums to [tex]\(180^\circ\)[/tex], the set of angles that could represent the interior angles of a triangle is:
[tex]\[ 26^\circ, 51^\circ, 103^\circ \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.