Question

1. refer to the diagram shown. determine the values of t and u. show or explain your thinking.
2. refer to the diagram shown. determine the values of a and b. show or explain your thinking.

Explanation:

Step1: Solve for $t$ (Q5)

First, find the straight angle complement of $149^\circ$:
$180^\circ - 149^\circ = 31^\circ$
This angle plus $3t$ and $50^\circ$ makes a right angle ($90^\circ$):
$31^\circ + 3t + 50^\circ = 90^\circ$
Simplify:
$81^\circ + 3t = 90^\circ$
$3t = 90^\circ - 81^\circ = 9^\circ$
$t = \frac{9^\circ}{3} = 3^\circ$

Step2: Solve for $u$ (Q5)

$u$ forms a straight angle with $149^\circ$ and $t$:
$u + 149^\circ + t = 180^\circ$
Substitute $t=3^\circ$:
$u = 180^\circ - 149^\circ - 3^\circ = 28^\circ$

Step3: Solve for $a$ (Q6)

First, find the vertical angle of $52^\circ$, then use the straight angle with $35^\circ$ and $a$:
$180^\circ - 52^\circ - 35^\circ - 90^\circ = a$
$a = 180^\circ - 177^\circ = 3^\circ$

Step4: Solve for $b$ (Q6)

$b$ is $a$ plus $3^\circ$ (from right angle check):
$b = 35^\circ + a = 35^\circ + 3^\circ = 38^\circ$
Or verify with right angle: $90^\circ - 52^\circ = 38^\circ$

Answer:

For Question 5:
$t = 3^\circ$, $u = 28^\circ$
For Question 6:
$a = 3^\circ$, $b = 38^\circ$