Question

in exercises 13 - 15, find the measure of each angle in the triangle. 13. 14. 15.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$.

Step2: Solve for $x$ in the first triangle (Exercise 13)

We have the equation $x+(x + 7)+127=180$.
Combining like - terms: $2x+134 = 180$.
Subtract 134 from both sides: $2x=180 - 134=46$.
Divide both sides by 2: $x = 23$.
So the angles are $x = 23^{\circ}$, $x + 7=23 + 7 = 30^{\circ}$, and $127^{\circ}$.

Step3: Solve for $x$ in the second triangle (Exercise 14)

We have the equation $x+(x + 38)+(x + 13)=180$.
Combining like - terms: $3x+51 = 180$.
Subtract 51 from both sides: $3x=180 - 51 = 129$.
Divide both sides by 3: $x = 43$.
So the angles are $x = 43^{\circ}$, $x + 38=43+38 = 81^{\circ}$, $x + 13=43 + 13 = 56^{\circ}$.

Step4: Solve for $x$ in the third triangle (Exercise 15)

We have a right - triangle, so $2x+(5x + 13)+90=180$.
Combining like - terms: $7x+103 = 180$.
Subtract 103 from both sides: $7x=180 - 103 = 77$.
Divide both sides by 7: $x = 11$.
So the angles are $2x=2\times11 = 22^{\circ}$, $5x + 13=5\times11+13 = 68^{\circ}$, and $90^{\circ}$.

Answer:

Exercise 13: $23^{\circ},30^{\circ},127^{\circ}$
Exercise 14: $43^{\circ},81^{\circ},56^{\circ}$
Exercise 15: $22^{\circ},68^{\circ},90^{\circ}$