Question

geometry
cii triangle sums skills practice
solve for x.
1)
right triangle with angles 70°, 3x+2° and right angle
2)
triangle with angles 60°, 70°, 4x+2°
find the measure of angle a.
3)
triangle with angles 66°, x+79°, x+49° (angle a is x+49°?)
4)
triangle with angles 50°, x+75°, x+65° (angle a is x+65°?)
name
date

Explanation:

1)

Step1: Use the triangle angle - sum property

In a right - triangle, the sum of the two non - right angles is \(90^{\circ}\). Also, for a triangle, the sum of all interior angles is \(180^{\circ}\). So, \(70+(3x + 2)=90\) (since one angle is \(90^{\circ}\)).

Step2: Solve the equation for \(x\)

Subtract \(70\) from both sides of the equation \(70+(3x + 2)=90\).
\(3x+2=90 - 70\)
\(3x+2 = 20\)
Subtract \(2\) from both sides: \(3x=20 - 2\)
\(3x=18\)
Divide both sides by \(3\): \(x=\frac{18}{3}=6\)

Step1: Apply the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(60 + 70+(4x + 2)=180\)

Step2: Solve the equation for \(x\)

First, simplify the left - hand side: \(130+(4x + 2)=180\)
\(4x+132 = 180\)
Subtract \(132\) from both sides: \(4x=180 - 132\)
\(4x=48\)
Divide both sides by \(4\): \(x=\frac{48}{4}=12\)

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(60+(x + 7)+(x + 49)=180\)

Step2: Simplify the equation

Combine like terms: \(60+x + 7+x + 49=180\)
\(2x+(60 + 7+49)=180\)
\(2x + 116=180\)

Step3: Solve for \(x\)

Subtract \(116\) from both sides: \(2x=180 - 116\)
\(2x=64\)
Divide by \(2\): \(x = 32\)

Step4: Find the measure of angle \(A\)

Angle \(A=x + 49\). Substitute \(x = 32\) into the expression: \(A=32+49=81^{\circ}\)

Answer:

\(x = 6\)

2)