Work out the size of angle a and angle b
1 answer:
Answer:
a = 120°
b = 60°
Step-by-step explanation:
Angle a and 60° are suplementary. The sum of supplementary angles is 180° (straight angle).
a + 60° = 180°
a = 180° - 60°
a = 120°
The sum of angles in the quadrilateral is 360°. Notice how two of the angles in the quadrilateral are marked as right angles (angles marked with a square). Each of them is 90°.
b + 90° + a + 90° = 360°
Substitute a with the value calculated in the previous step.
b + 90° + 120° + 90° = 360°
Solve for b.
b + 300° = 360°
b = 60°
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Answer:
Step-by-step explanation:
x = measure of the first angle
y = measure of the second angle
z = measure of the third angle
The sum of the measures of the second and third (y+z) is five times the measure of the first angle (=5x)
The third angle is 14 more than the second
And remember that the sum of these three angles must be equal to 180.
Let's take these equations
If you take a look at the first equation, we have y+z = 5x and we have y+z in the third equation as well, we can replace that....
Distribute the + sign
Combine like terms;
Divide by 6.
We have now defined that the measure of the first angle is 30º.
Let's take another equation... for example
I'm going to take this one because if I replace x and z in the third equation, all I'll have left will be y.
Distribute the + sign and Combine like terms;
Subtract 44 to isolate 2y.
Now divide by 2.
We already have the value of x and y. Once again, replacing this in the third equation will leave us with z to solve for.