Question

name triangles \tri\ these missing angles every triangle has a total angle measure of 180°. to find the measure of an unknown angle, add the two known angle measures and subtract their sum from 180°. 92° + 43° = 135° 180° - 135° = 45° x = 45° find the measure of each missing angle. a. b. c.

Explanation:

Step1: Calculate \( y \)

Sum of known angles: \( 42^{\circ}+90^{\circ}=132^{\circ} \)
Subtract from \( 180^{\circ} \): \( 180^{\circ}-132^{\circ}=48^{\circ} \), so \( y = 48^{\circ} \)

Step2: Calculate \( z \)

Sum of known angles: \( 60^{\circ}+60^{\circ}=120^{\circ} \)
Subtract from \( 180^{\circ} \): \( 180^{\circ}-120^{\circ}=60^{\circ} \), so \( z = 60^{\circ} \)

Step3: Calculate \( a \)

Sum of known angles: \( 78^{\circ}+78^{\circ}=156^{\circ} \)
Subtract from \( 180^{\circ} \): \( 180^{\circ}-156^{\circ}=24^{\circ} \), so \( a = 24^{\circ} \)

Step4: Calculate \( b \)

Sum of known angles: \( 37^{\circ}+93^{\circ}=130^{\circ} \)
Subtract from \( 180^{\circ} \): \( 180^{\circ}-130^{\circ}=50^{\circ} \), so \( b = 50^{\circ} \)

Step5: Calculate \( c \)

Sum of known angles: \( 107^{\circ}+39^{\circ}=146^{\circ} \)
Subtract from \( 180^{\circ} \): \( 180^{\circ}-146^{\circ}=34^{\circ} \), so \( c = 34^{\circ} \)

Step6: Calculate \( d \)

Sum of known angles: \( 73^{\circ}+59^{\circ}=132^{\circ} \)
Subtract from \( 180^{\circ} \): \( 180^{\circ}-132^{\circ}=48^{\circ} \), so \( d = 48^{\circ} \)

Step7: Calculate \( e \)

Sum of known angles: \( 31^{\circ}+15^{\circ}=46^{\circ} \)
Subtract from \( 180^{\circ} \): \( 180^{\circ}-46^{\circ}=134^{\circ} \), so \( e = 134^{\circ} \)

Step8: Calculate \( f \)

Sum of known angles: \( 49^{\circ}+69^{\circ}=118^{\circ} \)
Subtract from \( 180^{\circ} \): \( 180^{\circ}-118^{\circ}=62^{\circ} \), so \( f = 62^{\circ} \)

Step9: Calculate \( g \)

Sum of known angles: \( 98^{\circ}+41^{\circ}=139^{\circ} \)
Subtract from \( 180^{\circ} \): \( 180^{\circ}-139^{\circ}=41^{\circ} \), so \( g = 41^{\circ} \)

Answer:

\( y = 48^{\circ}\), \( z = 60^{\circ}\), \( a = 24^{\circ}\), \( b = 50^{\circ}\), \( c = 34^{\circ}\), \( d = 48^{\circ}\), \( e = 134^{\circ}\), \( f = 62^{\circ}\), \( g = 41^{\circ}\)