Question

3 activity: applying your rule work with a partner. use the rule you wrote in activity 2 to write an equation for each triangle. then solve the equation to find the value of x. use a protractor to check the reasonableness of your answer. a. triangle with 27°, 82°, x° b. triangle with 43°, 52°, x° c. triangle with 62.5°, 77°, x° d. triangle with 33.4°, 51.3°, x°

Explanation:

Part a

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(27^\circ + 82^\circ + x^\circ = 180^\circ\).

Step2: Simplify and solve for \(x\)

First, add \(27\) and \(82\): \(27 + 82 = 109\). Then, \(109 + x = 180\). Subtract \(109\) from both sides: \(x = 180 - 109 = 71\).

Step1: Apply angle sum property

For a triangle, \(43^\circ + 52^\circ + x^\circ = 180^\circ\).

Step2: Calculate and solve

Add \(43\) and \(52\): \(43 + 52 = 95\). Then, \(95 + x = 180\). Subtract \(95\): \(x = 180 - 95 = 85\).

Step1: Use triangle angle sum

The formula is \(62.5^\circ + 77^\circ + x^\circ = 180^\circ\).

Step2: Solve for \(x\)

Add \(62.5\) and \(77\): \(62.5 + 77 = 139.5\). Then, \(139.5 + x = 180\). Subtract \(139.5\): \(x = 180 - 139.5 = 40.5\).

Answer:

\(x = 71\)

Part b