Question

find the measure of each angle indicated.
15)
solve for x.
17)
find the measure of angle a.
19)
find the measure of each angle indicated.
21)
find the measure of angle a.
23)
26)

Explanation:

Step1: Recall triangle - angle sum property

The sum of the interior angles of a triangle is 180°.

Step2: Solve problem 15

Let the unknown angle be \(y\). Then \(y=180-(15 + 80)=85^{\circ}\)

Step3: Solve problem 16

Let the unknown angle be \(y\). Then \(y = 180-(70 + 70)=40^{\circ}\)

Step4: Solve problem 17

We know that \((x + 70)+70 + 41=180\). First, simplify the left - hand side: \(x+181 = 180\). Then \(x=180 - 181=-1\)

Step5: Solve problem 18

Since it is a right - triangle (\(90^{\circ}\) angle), we have \((x + 69)+25+90 = 180\). Simplify: \(x+184 = 180\), so \(x=-4\)

Step6: Solve problem 19

We have \((57 + x)+(x + 87)+60=180\). Combine like terms: \(2x+204 = 180\). Subtract 204 from both sides: \(2x=180 - 204=-24\). Then \(x=-12\)

Step7: Solve problem 20

We know that \((9x + 4)+(16x-4)+80 = 180\). Combine like terms: \(25x+80 = 180\). Subtract 80 from both sides: \(25x=100\). Divide by 25: \(x = 4\)

Step8: Solve problem 21

First, find the angle in the left - hand triangle. Let's call it \(a\), \(a=180-(30 + 100)=50^{\circ}\). Then, since the two triangles share a common angle, the unknown angle \(y\) in the right - hand triangle: \(y=180-(50 + 60)=70^{\circ}\)

Step9: Solve problem 22

The vertical angles are equal. Let the unknown angle be \(y\). We know that \(y+25+(40 + 30)=180\). Simplify: \(y+95 = 180\), so \(y = 85^{\circ}\)

Answer:

1. \(85^{\circ}\)
2. \(40^{\circ}\)
3. \(x=-1\)
4. \(x=-4\)
5. \(x=-12\)
6. \(x = 4\)
7. \(70^{\circ}\)
8. \(85^{\circ}\)