Question

asked Jun 17, 2024 205k views

1 Answer

Toon Casteele · Answer 1 · 2024-06-22T01:37:04+0000

Answer:

$\sf \angle 5 = 109^\circ$

$\sf \angle 8 = 71^\circ$

Explanation:

Given:

$\sf \angle 5 = (3x+7)^\circ$

$\sf \angle 8 = (2x+3)^\circ$

To find:

$\sf \angle 5 \textsf{ and } \angle 8$

Solution:

$\sf \angle 5 \textsf{ and } \angle 8$ are linear pairs.

Now, we can set up the expressions as:

$\sf \angle 5 + \angle 8 =180^\circ$

Since sum of angle of linear pair or straight line is 180°.

Substituting the value

$\sf (3x + 7) + (2x + 3) = 180$

Combine like terms.

$\sf 3x+7+2x+3=180$

$\sf 5x + 10 = 180$

Subtract 10 from both sides:

$\sf 5x = 180-10$

$\sf 5x=170$

Divide both sides of the equation by 5.

$\sf x=(170)/(5)$

$\sf x = 34$

Substitute 34 for x in the expressions:

$\sf \angle 5 = (3)(34) + 7 = 109^\circ$

$\sf \angle 8 = (2)(34) + 3 = 71^\circ$

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