Question

Find the unknown sizes of angles
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Answer 1

Answer:

R=50    b=130   a=135

Step-by-step explanation:

Sum of Internal angles   = 180

R= 180-85-45 = 50

missing interior angle R  = 50

If a side of a triangle is produced, then the exterior angle that is  formed is equal to the sum of the two interior opposite angles.

P+Q = 85+45= 130     b=130

P+R = 85+50 = 135     a=135

Answer 2

To solve this problem, we would have to add the sum of angles in a triangle and then find the missing side. Furthermore, value of R, a and b are 50°, 135° and 130° respectively.

Data;

• P = 85°
• Q = 45°
• a = ?
• b = ?

Sum of Angles in a Triangle

The sum of angles in a triangle is equal to 180° and we can find the missing side on R.

$P+Q+R = 180^0\\85^0+45^0+R = 180^0\\130^0+R=180^0\\R = 180 - 130 \\R = 50^0$

Since we know the value of R and Q, we can proceed to find a and b.

$Q+ a = 180$

The reason behind this is that the sum of angles on a straight line is equal to 180^0

$45+a = 180 \\a = 180 - 45 \\a = 135^0$

Now let's find the value of b

$R + b = 180\\R = 50^0\\50 + b = 180\\b = 180 - 50 \\b = 130$

From the calcuations above, the value of R, a and b are 50°, 135° and 130° respectively.

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