Question

Question

Use the Triangle Angle Sum Theorem to find the largest angle in a triangle with angle measures of (x−20)°
, (3x+3)°
, and (2x−7)°
.(1 point)
°

Answer 1

The Triangle Angle Sum Theorem states that the sum of the interior angles of a triangle is always ${180}^{\circ }$. Given the angles:

1. $(x-20{)}^{\circ }$
2. $(3x+3{)}^{\circ }$
3. $(2x-7{)}^{\circ }$

we can set up the equation:

$$(x-20)+(3x+3)+(2x-7)=180$$

Now, we simplify the left side:

$$x-20+3x+3+2x-7=180$$ $$(1x+3x+2x)+(-20+3-7)=180$$ $$6x-24=180$$

Next, we solve for $x$:

$$6x=180+24$$ $$6x=204$$ $$x=\frac{204}{6}$$ $$x=34$$

Now we substitute $x=34$ back into each angle:

1. First angle: $$(x-20)=34-20={14}^{\circ }$$

2. Second angle: $$(3x+3)=3(34)+3=102+3={105}^{\circ }$$

3. Third angle: $$(2x-7)=2(34)-7=68-7={61}^{\circ }$$

Now we have the measures of the three angles:

• ${14}^{\circ }$
• ${105}^{\circ }$
• ${61}^{\circ }$

The largest angle is:

$$\boxed{{\displaystyle {105}^{\circ }}}$$