Question

question 5
find the value of x.
figure is not to scale.
question 6
find the unknown angle measure.
figure is not to scale

Explanation:

Step1: Use triangle angle sum rule

The sum of angles in a triangle is $180^\circ$. The top triangle has a right angle ($90^\circ$) and $53^\circ$.
$x = 180 - 90 - 53$

Step2: Calculate the value

$x = 37$

Step3: Solve Question 5 angle sum

For the second triangle, sum of angles is $180^\circ$.
$x = 180 - 79 - 43$

Step4: Compute the result

$x = 58$

Step5: Identify isosceles triangle property

In the third triangle, two sides are equal, so the two marked angles are equal. Use angle sum rule.
$2x + 22 = 180$

Step6: Isolate and solve for x

$2x = 180 - 22$
$x = \frac{158}{2} = 79$

Answer:

Top question: $37^\circ$
Question 5: $58^\circ$
Question 6: $79^\circ$