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slega [8]
3 years ago
9

An exterior angle of a triangle is 152°. If the non-adjacent angles are congruent, then what are the measures of all of the inte

rior angles of the triangle?
a. 62°, 59°, 59°
b. 90°, 45°, 45°
c. 152°, 14°, 14°
d. 28°, 76°, 76°
Mathematics
1 answer:
nevsk [136]3 years ago
5 0

9514 1404 393

Answer:

  d.  28°, 76°, 76°

Step-by-step explanation:

The sum of the "non-adjacent" interior angles of the triangle is equal to the exterior angle, so is 152°. If those angles are congruent, each is half of 152°, or 76°. The remaining angle is the supplement to 152°, so is 180-152 = 28 degrees.

The interior angles are 28°, 76°, 76°.

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kodGreya [7K]

Step 1

Given;

Triangle\text{ TAG \textasciitilde Triangle BAG}

Required; To find the similarity postulate or theorem that applies.

Step 2

Both triangles share one side AG

They also have a common angle;

90^o

Side AG = 10 units and ∠AGT ≅ ∠AGB.

Thus, options A and B are discarded.

Step 3

Now, as for the SAS criteria, we need two sides to be congruent and their included angles to be congruent.

But, as no other information is given, we cannot determine whether the given triangles are congruent or not.

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4 0
1 year ago
Please solve this for me using substitution
Vinvika [58]

<h2> <u>Explanation</u><u>:</u></h2>

\bf \underline{★Given-} \\

\textsf{4x + 5y = 8};

\textsf{5x + 4y = 12}

\bf \underline{★To\: find-} \\

\textsf{the value of x and y in equation?}

\bf \underline{★Solution-} \\

\sf \leadsto 4x + 5y = 8 - - - (i)

\sf \leadsto 5x + 4y = 12 - - - (ii)

By first equation,

\sf \leadsto 4x + 5y = 8

\sf \leadsto 4x = 8 - 5y

\sf \leadsto x = \dfrac{8 - 5y}{4}

\textsf{Now, we can find the original value of Y.}\\

\sf \leadsto 5x + 4y = 12

\sf \leadsto 5 \bigg( \dfrac{8 - 5y}{4} \bigg) + 4y = 12

\sf \leadsto \dfrac{40 - 25y}{4} + 4y = 12

\sf \leadsto \dfrac{40 - 25y + 16y}{4} = 12

\sf \leadsto \dfrac{40 - 9y}{4} = 12

\sf \leadsto 40 - 9y = 12(4)

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\sf \leadsto y = \dfrac{ -8}{9}

\textsf{Now, we can find the original value of X.}\\

\sf \leadsto 4x + 5y = 8

\sf \leadsto  4x + 5 \bigg( \dfrac{ -8}{9} \bigg) = 8

\sf \leadsto 4x - \dfrac{40}{9} = 8

\sf \leadsto \dfrac{36x - 40}{9} = 8

\sf \leadsto 36x - 40 = 8(9)

\sf \leadsto 36x - 40 = 72

\sf \leadsto 36x = 72 + 40

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\underline{\textsf{Answer-}}\\

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6 0
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topjm [15]

Answer:

Step-by-step explanation:

Sweet. Get to answer finally. I was the guy commenting on your other post.

1. 72

2. 46

3. 99

4. Same side interior angles are supplementary

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so plug in your answer for y in the expression..

4(31)+3 = 127.

so angle 6 is 127

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