Answer:
Q1
<1=80°
<2=40°
<3=25°
Q2
<JKM=30.5°
Step-by-step explanation:
Q1
Angles at the centre of a circle standing on an arc measure, such as the way <1 stands on an arc measure of 80°, are equal to that arc measure:
<1=80°
An angle on the curve of a circle standing on an arc, such as <2, is half of an angle standing on the same arc at the centre, such as <1:
<2=0.5(<1)=0.5(80)=40°
The measure of a secant-secant angle, like <3, is one-half the difference of the measures of the intercepted arcs, in this case 30° and 80°.
<3=0.5(80-30)=0.5(50)=25°
Q2
Angles at the centre of a circle standing on an arc measure, are equal to that arc measure. So imagine an angle standing at the centre, sitting on the measure mML - it would equal 187°.
However since an angle on the curve of a circle standing on the same arc as an angle at the centre is half the angle at the centre, we can say that:
<MKL=(0.5)187=93.5
The angles along a straight line add to 180, so
<JKM+93.5+56=180
<JKM=180-149.5=30.5
